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%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.01",
%%% date = "08 August 2020",
%%% time = "10:28:01 MDT",
%%% filename = "ijnt.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "59233 51662 273405 2538126",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
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%%% of Number Theory (IJNT)",
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%%% Journal of Number Theory (IJFCS) (CODEN
%%% none, ISSN 1793-0421 (print), 1793-7310
%%% (electronic)), published by World
%%% Scientific.
%%%
%%% Publication began with volume 1, number 1, in
%%% March 2005, and the number of issues per
%%% volume has increased from 4 (2005--2007) to 6
%%% (2008) to 8 (2009--2015) to 10 (2016--).
%%%
%%% The journal has World-Wide Web site at
%%%
%%% http://ejournals.wspc.com.sg/ijnt
%%% https://www.worldscientific.com/worldscinet/ijnt
%%%
%%% At version 1.01, the COMPLETE year coverage
%%% looked like this:
%%%
%%% 2005 ( 37) 2011 ( 124) 2017 ( 154)
%%% 2006 ( 39) 2012 ( 119) 2018 ( 168)
%%% 2007 ( 39) 2013 ( 122) 2019 ( 132)
%%% 2008 ( 72) 2014 ( 125) 2020 ( 87)
%%% 2009 ( 89) 2015 ( 143)
%%% 2010 ( 111) 2016 ( 143)
%%%
%%% Article: 1704
%%%
%%% Total entries: 1704
%%%
%%% Data for the bibliography has been collected
%%% primarily from the journal Web site, with
%%% additional data entries from BibNet Project
%%% and TeX User Group bibliography archives.
%%%
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%%% journal are in French; English translations
%%% of titles are provided for them.
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%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-INT-J-NUMBER-THEORY = "International Journal of Number Theory (IJNT)"}
%%% ====================================================================
%%% Bibliography entries:
@Article{Bourgain:2005:MSP,
author = "J. Bourgain",
title = "More on the Sum--Product Phenomenon in Prime Fields
and Its Applications",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "1--32",
month = mar,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042105000108",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000108",
abstract = "In this paper we establish new estimates on
sum-product sets and certain exponential sums in finite
fields of prime order. Our first result is an extension
of the sum-product theorem from [8] when sets of
different sizes are involved. It is shown that if and
p$^{\varepsilon }$ < |B|, |C| < |A| < p$^{1 -
\varepsilon }$, then |A + B| + |A \cdotp C| >
p$^{\delta (\varepsilon)}$ |A|. Next we exploit the
Szemer{\'e}di--Trotter theorem in finite fields (also
obtained in [8]) to derive several new facts on
expanders and extractors. It is shown for instance that
the function f(x,y) = x(x+y) from to satisfies |F(A,B)|
> p$^{\beta }$ for some \beta = \beta (\alpha) > \alpha
whenever and $ |A| \sim |B| \sim p^\alpha $, $ 0 <
\alpha < 1$. The exponential sum $ \sum_{x \in A, y \in
B}$ \varepsilon$_p$ (axy+bx$^2$ y$^2$), ab \neq 0 (mod
p), may be estimated nontrivially for arbitrary sets
satisfying |A|, |B| > p$^{\rho }$ where \rho < 1/2 is
some constant. From this, one obtains an explicit
2-source extractor (with exponential uniform
distribution) if both sources have entropy ratio at
last \rho. No such examples when \rho < 1/2 seemed
known. These questions were largely motivated by recent
works on pseudo-randomness such as [2] and [3]. Finally
it is shown that if p$^{\varepsilon }$ < |A| < p$^{1 -
\varepsilon }$, then always |A + A|+|A$^{-1}$ +
A$^{-1}$ | > p$^{\delta (\varepsilon)}$ |A|. This is
the finite fields version of a problem considered in
[11]. If A is an interval, there is a relation to
estimates on incomplete Kloosterman sums. In the
Appendix, we obtain an apparently new bound on bilinear
Kloosterman sums over relatively short intervals
(without the restrictions of Karatsuba's result [14])
which is of relevance to problems involving the divisor
function (see [1]) and the distribution (mod p) of
certain rational functions on the primes (cf. [12]).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2005:EFQ,
author = "Heng Huat Chan and Zhi-Guo Liu and Say Tiong Ng",
title = "Elliptic Functions and the Quintuple, {Hirschhorn} and
{Winquist} Product Identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "33--43",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000017",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000017",
abstract = "In this article, we derive the quintuple, Hirschhorn
and Winquist product identities using the theory of
elliptic functions. Our method can be used to establish
generalizations of these identities due to the second
author.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alkan:2005:NRT,
author = "Emre Alkan and Alexandru Zaharescu",
title = "Nonvanishing of the {Ramanujan} {Tau} Function in
Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "45--51",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000029",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000029",
abstract = "We provide new estimates for the gap function of the
Delta function and for the number of nonzero values of
the Ramanujan tau function in short intervals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chen:2005:SEG,
author = "Sin-Da Chen and Sen-Shan Huang",
title = "On the series expansion of the {G{\"o}llnitz--Gordon}
continued fraction",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "53--63",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000030",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000030",
abstract = "We give combinatorial interpretations of the
coefficients in the series expansions of the
G{\"o}llnitz--Gordon continued fraction and its
reciprocal. These combinatorial results enable us to
determine the signs of the coefficients. At the end, we
also derive some interesting identities involving the
coefficients.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ivic:2005:MTS,
author = "Aleksandar Ivi{\'c}",
title = "The {Mellin} Transform of the Square of {Riemann}'s
Zeta-Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "65--73",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000042",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000042",
abstract = "Let. A result concerning analytic continuation of $
Z_1 $ (s) to {\mathbb{C}} is proved, and also a result
relating the order of to the order of.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ono:2005:APC,
author = "Ken Ono and Yuichiro Taguchi",
title = "$2$-Adic Properties of Certain Modular Forms and Their
Applications to Arithmetic Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "75--101",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000066",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000066",
abstract = "It is a classical observation of Serre that the Hecke
algebra acts locally nilpotently on the graded ring of
modular forms modulo 2 for the full modular group. Here
we consider the problem of classifying spaces of
modular forms for which this phenomenon continues to
hold. We give a number of consequences of this
investigation as they relate to quadratic forms,
partition functions, and central values of twisted
modular {$L$}-functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jenkins:2005:APT,
author = "Paul Jenkins",
title = "$p$-adic properties for traces of singular moduli",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "103--107",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S179304210500011X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210500011X",
abstract = "We examine the $p$-adic properties of Zagier's traces
$ \Tr (d)$ of the singular moduli of discriminant $ -
d$. In a recent preprint, Edixhoven proved that if $p$
is prime and $ \frac {-d}{p} = 1$, then $ \Tr (p^{2n}
d) \equiv 0 (\bmod p^n)$. We compute an exact formula
for $ \Tr (p^{2n}d)$ which immediately gives
Edixhoven's result as a corollary.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kedlaya:2005:LMA,
author = "Kiran S. Kedlaya",
title = "Local monodromy of $p$-adic differential equations: an
overview",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "109--154",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S179304210500008X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210500008X",
abstract = "This primarily expository article collects together
some facts from the literature about the monodromy of
differential equations on a $p$-adic (rigid analytic)
annulus, though often with simpler proofs. These
include Matsuda's classification of quasi-unipotent
\nabla -modules, the Christol--Mebkhout construction of
the ramification filtration, and the Christol--Dwork
Frobenius antecedent theorem. We also briefly discuss
the $p$-adic local monodromy theorem without proof.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Brueggeman:2005:NCN,
author = "Sharon Brueggeman",
title = "The Nonexistence of Certain Nonsolvable {Galois}
Extensions of Number Fields of Small Degree",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "1",
pages = "155--160",
month = mar,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000121",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000121",
abstract = "Serre's conjecture predicts the nonexistence of
certain nonsolvable Galois extensions of {$ \mathbb {Q}
$} which are unramified outside one small prime. These
nonexistence theorems have been proven by the
techniques of discriminant bounding. In this paper, we
will apply these techniques to nonsolvable extensions
of small degree number fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Choi:2005:STS,
author = "S. K. K. Choi and A. V. Kumchev and R. Osburn",
title = "On Sums of Three Squares",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "161--173",
month = jun,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042105000054",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000054",
abstract = "Let r$_3$ (n) be the number of representations of a
positive integer n as a sum of three squares of
integers. We give two alternative proofs of a
conjecture of Wagon concerning the asymptotic value of
the mean square of r$_3$ (n).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Adiga:2005:GRB,
author = "Chandrashekar Adiga and Shaun Cooper and Jung Hun
Han",
title = "A General Relation Between Sums of Squares and Sums of
Triangular Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "175--182",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000078",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000078",
abstract = "Let r$_k$ (n) and t$_k$ (n) denote the number of
representations of n as a sum of k squares, and as a
sum of k triangular numbers, respectively. We give a
generalization of the result r$_k$ (8n + k) = c$_k$
t$_k$ (n), which holds for 1 \leq k \leq 7, where c$_k$
is a constant that depends only on k. Two proofs are
provided. One involves generating functions and the
other is combinatorial.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Maier:2005:CGE,
author = "H. Maier and A. Sankaranarayanan",
title = "On a Certain General Exponential Sum",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "183--192",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000224",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000224",
abstract = "In this paper we study the general exponential sum
related to multiplicative functions $ f(n) $ with $
|f(n)| \leq 1 $, namely we study the sum $ F(x, \alpha)
= \sum_{n \leq x} f(n) e(n \alpha) $ and obtain a
non-trivial upper bound when $ \alpha $ is a certain
type of rational number.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Williams:2005:CS,
author = "Kenneth S. Williams",
title = "The Convolution Sum $ \sum_{m < n / 9} \sigma (m)
\sigma (n - 9 m) $",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "193--205",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000091",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000091",
abstract = "The evaluation of the sum $ \sum_{m < n / 9} \sigma
(m) \sigma (n - 9 m) $ is carried out for all positive
integers $n$. This evaluation is used to detemine the
number of solutions to $ n = x_1^2 + x_1 x_2 + x_2^2 +
x_3^2 + x_3 x_4 + x_4^2 + 3 (x_5^2 + x_5 x_6 + x_6^2 +
x_7^2 + x_7 x_8 + x_8^2)$ in integers $ x_1$, $ x_2$, $
x_3$, $ x_4$, $ x_5$, $ x_6$, $ x_7$, $ x_8$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2005:HMP,
author = "Tsz Ho Chan",
title = "Higher Moments of Primes in Short Intervals {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "207--214",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000169",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000169",
abstract = "Given good knowledge on the even moments, we derive
asymptotic formulas for \lambda th moments of primes in
short intervals and prove ``equivalence'' result on odd
moments. We also provide numerical evidence in support
of these results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lovejoy:2005:TSC,
author = "Jeremy Lovejoy",
title = "A Theorem on Seven-Colored Overpartitions and Its
Applications",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "215--224",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000157",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000157",
abstract = "A $q$-series identity in four parameters is
established and interpreted as a statement about
7-colored overpartitions. As corollaries some
overpartition theorems of the Rogers--Ramanujan type
and some weighted overpartition theorems are exhibited.
Among these are overpartition analogues of classical
partition theorems of Schur and G{\"o}llnitz.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Eie:2005:EGE,
author = "Minking Eie and Wen-Chin Liaw and Fu-Yao Yang",
title = "On Evaluation of Generalized {Euler} Sums of Even
Weight",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "225--242",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000182",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000182",
abstract = "The classical Euler sum $ S_{p, q} = \sum_{k =
1}^\infty \frac {1}{k^q} \sum_{j = 1}^k \frac {1}{j^p}
$ cannot be evaluated when the weight $ p + q $ is even
unless $ p = 1 $ or $ p = q $ or $ (p, q) = (2, 4) $ or
$ (p, q) = (4, 2) $ [7]. However it is a different
story if instead we consider the alternating sums $
G_{p, q}^{-, -} = \sum_{k = 0}^\infty \frac {( -
1)^k}{(2 k + 1)^q} \sum_{j = 1}^k \frac {( - 1)^{j +
1}}{j^p} $ and $ G_{p, q}^{+, -} = \sum_{k = 0}^\infty
\frac {( - 1)^k}{(2 k + 1)^q} \sum_{j = 1}^k \frac
{1}{j^p} $. They can be evaluated for even weight $ p +
q $. In this paper, we shall evaluate a family of
generalized Euler sums containing $ G_{p, q}^{-, -} $
when the weight $ p + q $ is even via integral
transforms of Bernoulli identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Delaunay:2005:MOT,
author = "Christophe Delaunay",
title = "Moments of the Orders of {Tate--Shafarevich} Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "243--264",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000133",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000133",
abstract = "We give some conjectures for the moments of the orders
of the Tate--Shafarevich groups of elliptic curves
belonging to a family of quadratic twists. These
conjectures follow from the predictions on
{$L$}-functions given by the random matrix theory
[12,5] and from the Birch and Swinnerton--Dyer
conjecture. Furthermore, including the Cohen--Lenstra
type heuristics for Tate--Shafarevich groups, we obtain
some conjectural estimates for the regulator of rank 1
elliptic curves in a family of quadratic twists.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baier:2005:LSI,
author = "Stephan Baier and Liangyi Zhao",
title = "Large Sieve Inequality with Characters for Powerful
Moduli",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "265--279",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000170",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000170",
abstract = "In this paper we aim to generalize the results in [1,
2, 19] and develop a general formula for large sieve
with characters to powerful moduli that will be an
improvement to the result in [19].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Petsche:2005:QVB,
author = "Clayton Petsche",
title = "A Quantitative Version of {Bilu}'s Equidistribution
Theorem",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "281--291",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000145",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000145",
abstract = "We use Fourier-analytic methods to give a new proof of
Bilu's theorem on the complex equidistribution of small
points on the one-dimensional algebraic torus. Our
approach yields a quantitative bound on the error term
in terms of the height and the degree.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baoulina:2005:PC,
author = "Ioulia Baoulina",
title = "On a Problem of {Carlitz}",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "2",
pages = "293--307",
month = jun,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000194",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:12 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000194",
abstract = "Let $ N_q $ be the number of solutions to the equation
$ (x_1 + \cdots + x_n)^2 = a x_1 \ldots {} x_n $ over
the finite field $ \mathbb {F}_q = \mathbb {F}_p $.
Carlitz found formulas for $ N_q $ when $ n = 3 $ or
$4$. In an earlier paper, we found formulas for $ N_q$
when $ d = \gcd (n 2, q - 1) = 1$ or $2$ or $3$ or $4$;
and when there exists an $l$ such that $ p^l - 1 (\bmod
d)$. In another paper the cases $ d = 7$ or $ 14$, $ p
2$ or $4$ $ (\bmod 7)$ were considered. In this paper,
we find formulas for $ N_q$ when $ d = 8$. We also
simplify formulas for $ N_q$ when $ d = 4$, $ p 1$ $
(\bmod 4)$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bugeaud:2005:PPL,
author = "Yann Bugeaud and Florian Luca and Maurice Mignotte and
Samir Siksek",
title = "On Perfect Powers in {Lucas} Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "309--332",
month = sep,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042105000236",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000236",
abstract = "Let (u$_n$)$_{n \geq 0}$ be the binary recurrence
sequence of integers given by u$_0$ = 0, u$_1$ = 1 and
u$_{n + 2}$ = 2(u$_{n + 1}$ + u$_n$). We show that the
only positive perfect powers in this sequence are u$_1$
= 1 and u$_4$ = 16. We further discuss the problem of
determining perfect powers in Lucas sequences in
general.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Beck:2005:DAG,
author = "Matthias Beck and Bruce C. Berndt and O-Yeat Chan and
Alexandru Zaharescu",
title = "Determinations of Analogues of {Gauss} Sums and Other
Trigonometric Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "333--356",
month = sep,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000200",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000200",
abstract = "Explicit determinations of several classes of
trigonometric sums are given. These sums can be viewed
as analogues or generalizations of Gauss sums. In a
previous paper, two of the present authors considered
primarily sine sums associated with primitive odd
characters. In this paper, we establish two general
theorems involving both sines and cosines, with more
attention given to cosine sums in the several examples
that we provide.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Roy:2005:SAC,
author = "Damien Roy",
title = "Simultaneous Approximation by Conjugate Algebraic
Numbers in Fields of Transcendence Degree One",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "357--382",
month = sep,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000212",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000212",
abstract = "We present a general result of simultaneous
approximation to several transcendental real, complex
or $p$-adic numbers \xi$_1$, \ldots, \xi$_t$ by
conjugate algebraic numbers of bounded degree over {$
\mathbb {Q}$}, provided that the given transcendental
numbers \xi$_1$, \ldots, \xi$_t$ generate over {$
\mathbb {Q}$} a field of transcendence degree one. We
provide sharper estimates for example when \xi$_1$,
\ldots, \xi$_t$ form an arithmetic progression with
non-zero algebraic difference, or a geometric
progression with non-zero algebraic ratio different
from a root of unity. In this case, we also obtain by
duality a version of Gel'fond's transcendence criterion
expressed in terms of polynomials of bounded degree
taking small values at \xi$_1$, \ldots, \xi$_t$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alkan:2005:AFS,
author = "Emre Alkan and Alexandru Zaharescu and Mohammad Zaki",
title = "Arithmetical Functions in Several Variables",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "383--399",
month = sep,
year = "2005",
DOI = "https://doi.org/10.1142/S179304210500025X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210500025X",
abstract = "In this paper we investigate the ring A$_r$ (R) of
arithmetical functions in r variables over an integral
domain R. We study a class of absolute values, and a
class of derivations on A$_r$ (R). We show that a
certain extension of A$_r$ (R) is a discrete valuation
ring. We also investigate the metric structure of the
ring A$_r$ (R).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Suzuki:2005:RBZ,
author = "Masatoshi Suzuki",
title = "A Relation Between the Zeros of Two Different
{$L$}-Functions Which Have an {Euler} Product and
Functional Equation",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "401--429",
month = sep,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000248",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000248",
abstract = "As automorphic {$L$}-functions or Artin
{$L$}-functions, several classes of {$L$}-functions
have Euler products and functional equations. In this
paper we study the zeros of {$L$}-functions which have
Euler products and functional equations. We show that
there exists a relation between the zeros of the
Riemann zeta-function and the zeros of such
{$L$}-functions. As a special case of our results, we
find relations between the zeros of the Riemann
zeta-function and the zeros of automorphic
{$L$}-functions attached to elliptic modular forms or
the zeros of Rankin--Selberg {$L$}-functions attached
to two elliptic modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Niederreiter:2005:ESD,
author = "Harald Niederreiter and Arne Winterhof",
title = "Exponential sums and the distribution of inversive
congruential pseudorandom numbers with power of two
modulus",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "431--438",
month = sep,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042105000261",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11K38 (11K45 11L07)",
MRnumber = "2175100 (2006f:11092)",
MRreviewer = "Igor E. Shparlinski",
bibdate = "Thu Dec 22 06:50:44 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000261",
abstract = "Niederreiter and Shparlinski obtained a nontrivial
discrepancy bound for sequences of inversive
congruential pseudorandom numbers with odd prime-power
modulus. Because of technical difficulties they had to
leave open the case of greatest practical interest,
namely where the modulus is a power of 2. In the
present paper we successfully treat this case by using
recent advances in the theory of exponential sums.",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Number Theory",
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Eie:2005:EDE,
author = "Minking Eie and Yao Lin Ong and Fu Yao Yang",
title = "Evaluating Double {Euler} Sums Over Rationally
Deformed Simplices",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "3",
pages = "439--458",
month = sep,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000273",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000273",
abstract = "As a natural generalization of the classical Euler sum
defined by $ S_{p, q} = \sum_{k = 1}^\infty \frac
{1}{k^q} \sum_{j = 1}^k \frac {1}{j^p} $, we change the
upper limit of the inner summation into $ k r $, a
fixed rational multiple of $k$, and obtain countable
families of new sums which we call the extended Euler
sums. We shall develop a systematic new method to
evaluate these extended Euler sums as well as
corresponding alternating sums in terms of values at
non-negative integers of cosine and sine parts of the
periodic zeta function when the weight $ p + q$ is
odd.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Friedlander:2005:IS,
author = "J. B. Friedlander and H. Iwaniec",
title = "The Illusory Sieve",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "459--494",
month = dec,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042105000303",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000303",
abstract = "We study some of the extremely strong statements that
can be made about the distribution of primes assuming
the (unlikely) existence of exceptional Dirichlet
characters. We treat this in general and then apply the
results to the particular cases of primes of the form $
a^2 + b^6 $ and of elliptic curves having prime
discriminant.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Edixhoven:2005:AGT,
author = "Bas Edixhoven",
title = "On the $p$-adic geometry of traces of singular
moduli",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "495--497",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000327",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000327",
abstract = "The aim of this article is to show that $p$-adic
geometry of modular curves is useful in the study of
$p$-adic properties of {\em traces\/} of singular
moduli. In order to do so, we partly answer a question
by Ono [7, Problem 7.30]. As our goal is just to
illustrate how $p$-adic geometry can be used in this
context, we focus on a relatively simple case, in the
hope that others will try to obtain the strongest and
most general results. For example, for p = 2, a result
stronger than Theorem 2 is proved in [2], and a result
on some modular curves of genus zero can be found in
[8]. It should be easy to apply our method, because of
its local nature, to modular curves of arbitrary level,
as well as to Shimura curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Litsyn:2005:IFS,
author = "Simon Litsyn and Vladimir Shevelev",
title = "Irrational factors satisfying the little {Fermat}
theorem",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "499--512",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000339",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000339",
abstract = "We study possible generalizations of the little Fermat
theorem when the base of the exponentiation is allowed
to be a non-integer. Such bases we call Fermat factors.
We attempt classification of Fermat factors, and
suggest several constructions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dummigan:2005:RTO,
author = "Neil Dummigan",
title = "Rational Torsion on Optimal Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "513--531",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000340",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000340",
abstract = "Vatsal has proved recently a result which has
consequences for the existence of rational points of
odd prime order \ell on optimal elliptic curves over {$
\mathbb {Q} $}. When the conductor N is squarefree,
\ell \nmid N and the local root number w$_p$ = -1 for
at least one prime p | N, we offer a somewhat different
proof, starting from an explicit cuspidal divisor on
X$_0$ (N). We also prove some results linking the
vanishing of L(E,1) with the divisibility by \ell of
the modular parametrization degree, fitting well with
the Bloch--Kato conjecture for L(Sym$^2$ E,2), and with
an earlier construction of elements in
Shafarevich--Tate groups. Finally (following Faltings
and Jordan) we prove an analogue of the result on \ell
-torsion for cuspidal Hecke eigenforms of level one
(and higher weight), thereby strengthening some
existing evidence for another case of the Bloch--Kato
conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Long:2005:SPM,
author = "Ling Long and Yifan Yang",
title = "A Short Proof of {Milne}'s Formulas for Sums of
Integer Squares",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "533--551",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000364",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000364",
abstract = "We give a short proof of Milne's formulas for sums of
4n$^2$ and 4n$^2$ + 4n integer squares using the theory
of modular forms. Other identities of Milne are also
discussed.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mollin:2005:EAL,
author = "R. A. Mollin",
title = "On an Elementary Approach to the {Lebesgue--Nagell}
Equation",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "553--561",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000352",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000352",
abstract = "We discuss the feasibility of an elementary solution
to the Diophantine equation of the form x$^2$ + D =
y$^n$, where D > 1, n \geq 3 and x > 0, called the
Lebesgue--Nagell equation, which has recently been
solved for 1 \leq D \leq 100 in [1].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knopfmacher:2005:SFC,
author = "A. Knopfmacher and M. E. Mays",
title = "A Survey of Factorization Counting Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "563--581",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000315",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000315",
abstract = "The general field of additive number theory considers
questions concerning representations of a given
positive integer n as a {\em sum\/} of other integers.
In particular, {\em partitions\/} treat the sums as
unordered combinatorial objects, and {\em
compositions\/} treat the sums as ordered. Sometimes
the sums are restricted, so that, for example, the
summands are distinct, or relatively prime, or all
congruent to \pm 1 modulo 5. In this paper we review
work on analogous problems concerning representations
of n as a {\em product\/} of positive integers. We
survey techniques for enumerating product
representations both in the unrestricted case and in
the case when the factors are required to be distinct,
and both when the product representations are
considered as ordered objects and when they are
unordered. We offer some new identities and
observations for these and related counting functions
and derive some new recursive algorithms to generate
lists of factorizations with restrictions of various
types.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Luca:2005:PDL,
author = "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}",
title = "Prime Divisors of {Lucas} Sequences and a Conjecture
of {Ska{\l}ba}",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "583--591",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000285",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000285",
abstract = "In this paper, we give some heuristics suggesting that
if (u$_n$)$_{n \geq 0}$ is the Lucas sequence given by
u$_n$ = (a$^n$- 1)/(a - 1), where a > 1 is an integer,
then \omega (u$_n$) \geq (1 + o(1))log n log log n
holds for almost all positive integers n.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhang:2005:EET,
author = "Liang-Cheng Zhang",
title = "Explicit Evaluations of Two {Ramanujan--Selberg}
Continued Fractions",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "593--601",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000297",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000297",
abstract = "This paper gives explicit evaluations for two
Ramanujan--Selberg continued fractions in terms of
class invariants and singular moduli.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2005:AIV,
author = "Anonymous",
title = "Author Index (Volume 1)",
journal = j-INT-J-NUMBER-THEORY,
volume = "1",
number = "4",
pages = "603--605",
month = dec,
year = "2005",
DOI = "https://doi.org/10.1142/S1793042105000376",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:13 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042105000376",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kohnen:2006:TSA,
author = "Winfried Kohnen and Riccardo Salvati Manni",
title = "On the Theta Series Attached to {$ D_m^+ $}-Lattices",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "1--5",
month = mar,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042106000449",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000449",
abstract = "We show that the theta series attached to the -lattice
for any positive integer divisible by 8 can be
explicitly expressed as a finite rational linear
combination of products of two Eisenstein series.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cohen:2006:PRQ,
author = "Joseph Cohen",
title = "Primitive Roots in Quadratic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "7--23",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000425",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000425",
abstract = "We consider an analogue of Artin's primitive root
conjecture for units in real quadratic fields. Given
such a nontrivial unit, for a rational prime p which is
inert in the field the maximal order of the unit modulo
p is p + 1. An extension of Artin's conjecture is that
there are infinitely many such inert primes for which
this order is maximal. This is known at present only
under the Generalized Riemann Hypothesis.
Unconditionally, we show that for any choice of 7 units
in different real quadratic fields satisfying a certain
simple restriction, there is at least one of the units
which satisfies the above version of Artin's
conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vulakh:2006:DA,
author = "L. Ya. Vulakh",
title = "{Diophantine} approximation in {$ Q(\sqrt {-5}) $} and
{$ Q(\sqrt {-5}) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "25--48",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000462",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000462",
abstract = "The complete description of the discrete part of the
Lagrange and Markov spectra of the imaginary quadratic
fields with discriminants -20 and -24 are given. Farey
polygons associated with the extended Bianchi groups
B$_d$, d = 5, 6, are used to reduce the problem of
finding the discrete part of the Markov spectrum for
the group B$_d$ to the corresponding problem for one of
its maximal Fuchsian subgroup. Hermitian points in the
Markov spectrum of B$_d$ are introduced for any d. Let
H$^3$ be the upper half-space model of the
three-dimensional hyperbolic space. If \nu is a
Hermitian point in the spectrum, then there is a set of
extremal geodesics in H$^3$ with diameter 1/\nu, which
depends on one continuous parameter. This phenomenon
does not take place in the hyperbolic plane.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Thong:2006:CFG,
author = "Nguyen Quang Do Thong",
title = "Sur la conjecture faible de {Greenberg} dans le cas
ab{\'e}lien $p$-d{\'e}compos{\'e}. ({French}) [{On} the
weak conjecture of {Greenberg} in the abelian
$p$-decomposed case]",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "49--64",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000395",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000395",
abstract = "Let p be an odd prime. For any CM number field K
containing a primitive pth root of unity, class field
theory and Kummer theory put together yield the well
known reflection inequality \lambda$^+$ \leq
\lambda$^-$ between the ``plus'' and ``minus'' parts of
the \lambda -invariant of K. Greenberg's classical
conjecture predicts the vanishing of \lambda$^+$. We
propose a weak form of this conjecture: \lambda$^+$ =
\lambda$^-$ if and only if \lambda$^+$ = \lambda$^-$ =
0, and we prove it when K$^+$ is abelian, p is totally
split in K$^+$, and certain conditions on the
cohomology of circular units are satisfied (e.g. in the
semi-simple case).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Borwein:2006:TTG,
author = "Jonathan M. Borwein and David M. Bradley",
title = "Thirty-two {Goldbach} variations",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "65--103",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000383",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11M41 (11M06)",
MRnumber = "2217795",
MRreviewer = "F. Beukers",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "http://docserver.carma.newcastle.edu.au/301/;
https://www.worldscientific.com/doi/10.1142/S1793042106000383",
abstract = "We give thirty-two diverse proofs of a small
mathematical gem --- the fundamental Euler sum identity
$ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar {2}, 1) $.
We also discuss various generalizations for multiple
harmonic (Euler) sums and some of their many
connections, thereby illustrating both the wide variety
of techniques fruitfully used to study such sums and
the attraction of their study.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2006:TTG",
}
@Article{Chan:2006:NPS,
author = "Tsz Ho Chan",
title = "A Note on Primes in Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "105--110",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000437",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000437",
abstract = "Montgomery and Soundararajan obtained evidence for the
Gaussian distribution of primes in short intervals
assuming a quantitative Hardy--Littlewood conjecture.
In this article, we show that their methods may be
modified and an average form of the Hardy--Littlewood
conjecture suffices.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Takloo-Bighash:2006:RPA,
author = "Ramin Takloo-Bighash",
title = "A Remark on a Paper of {Ahlgren}, {Berndt}, {Yee}, and
{Zaharescu}",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "111--114",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000450",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000450",
abstract = "A classical theorem of Ramanujan relates an integral
of Dedekind eta-function to a special value of a
Dirichlet {$L$}-function at s = 2. Ahlgren, Berndt, Yee
and Zaharescu have generalized this result [1]. In this
paper, we generalize this result to the context of
holomorphic cusp forms on the upper half space.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cooper:2006:QPI,
author = "Shaun Cooper",
title = "The Quintuple Product Identity",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "115--161",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000401",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000401",
abstract = "The quintuple product identity was first discovered
about 90 years ago. It has been published in many
different forms, and at least 29 proofs have been
given. We shall give a comprehensive survey of the work
on the quintuple product identity, and a detailed
analysis of the many proofs.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{El-Mahassni:2006:DNC,
author = "Edwin D. El-Mahassni and Arne Winterhof",
title = "On the Distribution of Nonlinear Congruential
Pseudorandom Numbers in Residue Rings",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "163--168",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000413",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000413",
abstract = "The nonlinear congruential method is an attractive
alternative to the classical linear congruential method
for pseudorandom number generation. In this paper we
present a new type of discrepancy bound for sequences
of s-tuples of successive nonlinear congruential
pseudorandom numbers over a ring of integers
{\mathbb{Z}}$_M$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Walling:2006:AHO,
author = "Lynne H. Walling",
title = "Action of {Hecke} Operators on {Siegel} Theta Series
{I}",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "169--186",
month = jun,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042106000516",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000516",
abstract = "We apply the Hecke operators T(p) and to a degree n
theta series attached to a rank 2k {\mathbb{Z}}-lattice
L, n \leq k, equipped with a positive definite
quadratic form in the case that L/pL is hyperbolic. We
show that the image of the theta series under these
Hecke operators can be realized as a sum of theta
series attached to certain closely related lattices,
thereby generalizing the Eichler Commutation Relation
(similar to some work of Freitag and of Yoshida). We
then show that the average theta series (averaging over
isometry classes in a given genus) is an eigenform for
these operators. We show the eigenvalue for T(p) is \in
(k - n, n), and the eigenvalue for T\prime$_j$ (p$^2$)
(a specific linear combination of T$_0$ (p$^2$),\ldots,
T$_j$ (p$^2$)) is p$^{j(k - n) + j(j - 1) / 2}$ \beta
(n,j)\in (k-j,j) where \beta (*,*), \in (*,*) are
elementary functions (defined below).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bringmann:2006:BBA,
author = "Kathrin Bringmann and Benjamin Kane and Winfried
Kohnen",
title = "On the Boundary Behavior of Automorphic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "187--194",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000565",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000565",
abstract = "We investigate the boundary behavior of modular forms
f on the full modular group. We first show that $ \{ x
\in [0, 1] | \lim_{y \rightarrow 0^+} y^{k / 2} |f(x +
i y)| \mathrm {exists} \} $ is contained in a set of
Lebesgue measure 0. In particular, we recover the
well-known fact that the real axis is a natural
boundary of definition for f. On the other hand, using
the Rankin--Selberg Dirichlet series attached to f, we
show that taking the limit over the ``average'' over
all x \in [0,1] behaves ``well''. Our results also
apply to Maass wave forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bennett:2006:GTB,
author = "Michael A. Bennett and Alain Togb{\'e} and P. G.
Walsh",
title = "A Generalization of a Theorem of {Bumby} on Quartic
{Diophantine} Equations",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "195--206",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000474",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000474",
abstract = "Bumby proved that the only positive integer solutions
to the quartic Diophantine equation 3X$^4$- 2Y$^2$ = 1
are (X, Y) = (1, 1),(3, 11). In this paper, we use
Thue's hypergeometric method to prove that, for each
integer m \geq 1, the only positive integers solutions
to the Diophantine equation (m$^2$ + m + 1)X$^4$-
(m$^2$ + m)Y$^2$ = 1 are (X,Y) = (1, 1),(2m + 1, 4m$^2$
+ 4m + 3).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Laishram:2006:GCC,
author = "Shanta Laishram and T. N. Shorey",
title = "{Grimm}'s Conjecture on Consecutive Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "207--211",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000498",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000498",
abstract = "For positive integers n and k, it is possible to
choose primes P$_1$, P$_2$, \ldots, P$_k$ such that
P$_i$ | (n + i) for 1 \leq i \leq k whenever n + 1, n +
2,\ldots, n + k are all composites and n \leq 1.9 $
\times $ 10$^{10}$. This provides a numerical
verification of Grimm's Conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hirschhorn:2006:CMS,
author = "Michael D. Hirschhorn",
title = "The Case of the Mysterious Sevens",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "213--216",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000486",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000486",
abstract = "We give a simple, direct proof of a theorem involving
partitions into distinct parts, where multiples of 7
come in two colours.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bremner:2006:TRP,
author = "Andrew Bremner and Richard K. Guy",
title = "Triangle-Rectangle Pairs with a Common Area and a
Common Perimeter",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "217--223",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000504",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000504",
abstract = "We solve a problem of Bill Sands, to find pairs of
Heron triangles and rectangles, such as (5,5,6) & [2 $
\times $ 6] or (13,20,21) & [6 $ \times $ 21] which
have a common area and a common perimeter. The original
question was posed for right-angled triangles, but
there are no nondegenerate such. There are infinitely
many isosceles triangles and these have been exhibited
by Guy. Here we solve the general problem; the
triangle-rectangle pairs are parametrized by a family
of elliptic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tolev:2006:DTS,
author = "D. I. Tolev",
title = "On the distribution of $r$-tuples of squarefree
numbers in short intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "225--234",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S179304210600053X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210600053X",
abstract = "We consider the number of r-tuples of squarefree
numbers in a short interval. We prove that it cannot be
much bigger than the expected value and we also
establish an asymptotic formula if the interval is not
very short.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Spearman:2006:DCC,
author = "Blair K. Spearman and Kenneth S. Williams",
title = "On the Distribution of Cyclic Cubic Fields with Index
$2$",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "235--247",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000541",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000541",
abstract = "In this paper we prove an analogue of Mertens' theorem
for primes of each of the forms a$^2$ +27b$^2$ and
4a$^2$ +2ab+7b$^2$ and then use this result to
determine an asymptotic formula for the number of
positive integers n \leq x which are discriminants of
cyclic cubic fields with each such field having field
index 2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Grekos:2006:VTC,
author = "G. Grekos and L. Haddad and C. Helou and J. Pihko",
title = "Variations on a Theme of {Cassels} for Additive
Bases",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "249--265",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000553",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000553",
abstract = "We introduce the notion of caliber, cal(A, B), of a
strictly increasing sequence of natural numbers A with
respect to another one B, as the limit inferior of the
ratio of the nth term of A to that of B. We further
consider the limit superior t(A) of the average order
of the number of representations of an integer as a sum
of two elements of A. We give some basic properties of
each notion and we relate the two together, thus
yielding a generalization, of the form t(A) \leq
t(B)/cal(A, B), of a result of Cassels specific to the
case where A is an additive basis of the natural
numbers and B is the sequence of perfect squares. We
also provide some formulas for the computation of t(A)
in a large class of cases, and give some examples.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kowalski:2006:RQT,
author = "E. Kowalski",
title = "On the Rank of Quadratic Twists of Elliptic Curves
Over Function Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "267--288",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000528",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000528",
abstract = "We prove quantitative upper bounds for the number of
quadratic twists of a given elliptic curve E/F$_q$ (C)
over a function field over a finite field that have
rank \geq 2, and for their average rank. The main tools
are constructions and results of Katz and uniform
versions of the Chebotarev density theorem for
varieties over finite fields. Moreover, we
conditionally derive a bound in some cases where the
degree of the conductor is unbounded.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gaborit:2006:ELG,
author = "Philippe Gaborit and Ann Marie Natividad and Patrick
Sol{\'e}",
title = "{Eisenstein} Lattices, {Galois} Rings and Quaternary
Codes",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "289--303",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000577",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000577",
abstract = "Self-dual codes over the Galois ring GR(4,2) are
investigated. Of special interest are quadratic double
circulant codes. Euclidean self-dual (Type II) codes
yield self-dual (Type II) {\mathbb{Z}}$_4$-codes by
projection on a trace orthogonal basis. Hermitian
self-dual codes also give self-dual {\mathbb{Z}}$_4$
codes by the cubic construction, as well as Eisenstein
lattices by Construction A. Applying a suitable Gray
map to self-dual codes over the ring gives formally
self-dual {$ \mathbb {F} $}$_4$-codes, most notably in
length 12 and 24. Extremal unimodular lattices in
dimension 38, 42 and the first extremal 3-modular
lattice in dimension 44 are constructed.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Loh:2006:ACP,
author = "Po-Ru Loh and Robert C. Rhoades",
title = "$p$-adic and combinatorial properties of modular form
coefficients",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "2",
pages = "305--328",
month = jun,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000590",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000590",
abstract = "For two particular classes of elliptic curves, we
establish congruences relating the coefficients of
their corresponding modular forms to combinatorial
objects. These congruences resemble a supercongruence
for the Ap{\'e}ry numbers conjectured by Beukers and
proved by Ahlgren and Ono in [1]. We also consider the
trace Tr$_{2k}$ (\Gamma$_0$ (N), n) of the Hecke
operator T$_n$ acting on the space of cusp forms
S$_{2k}$ (\Gamma$_0$ (N)). We show that for (n, N) = 1,
these traces interpolate $p$-adically in the weight
aspect.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Flicker:2006:TCS,
author = "Yuval Z. Flicker and Dmitrii Zinoviev",
title = "Twisted Character of a Small Representation of {$
\mathrm {Gl}(4) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "329--350",
month = sep,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042106000589",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000589",
abstract = "We compute by a purely local method the (elliptic) $
\theta $-twisted character $ \chi_{\pi Y}$ of the
representation \pi_Y = I_{(3, 1)} (1_3 \times \chi_Y)
of G = GL(4, F), where F is a $p$-adic field, p \neq 2,
and Y is an unramified quadratic extension of F; \chi_Y
is the nontrivial character of F^{\times} /N_{Y/F}
Y^{\times}. The representation \pi_Y is normalizedly
induced from, m_i \in GL(i, F), on the maximal
parabolic subgroup of type (3, 1); \theta is the
``transpose-inverse'' involution of G. We show that the
twisted character \chi_{\pi Y} of \pi_Y is an unstable
function: its value at a twisted regular elliptic
conjugacy class with norm in C_Y = C_Y (F)=``(GL(2,
Y)/F^{\times})_F is minus its value at the other class
within the twisted stable conjugacy class. It is 0 at
the classes without norm in C_Y. Moreover \pi_Y is the
endoscopic lift of the trivial representation of C_Y.
We deal only with unramified Y/F, as globally this case
occurs almost everywhere. The case of ramified Y/F
would require another paper. Our C_Y = ``(R_{Y/F}
GL(2)/GL(1))_F '' has Y-points C_Y (Y) = {(g, g\prime)
\in GL(2, Y) \times GL(2, Y); det(g) =
det(g\prime)}/Y^{\times} (Y^{\times} embeds
diagonally); \sigma(\neq 1) in Gal(Y/F) acts by \sigma
(g, g\prime) = (\sigma g\prime, \sigma g). It is a
\theta -twisted elliptic endoscopic group of GL(4).
Naturally this computation plays a role in the theory
of lifting of C_Y and GSp(2) to GL(4) using the trace
formula, to be discussed elsewhere. Our work extends
--- to the context of nontrivial central characters ---
the work of [7], where representations of PGL(4, F) are
studied. In [7] we develop a 4-dimensional analogue of
the model of the small representation of PGL(3, F)
introduced by the first author and Kazhdan in [5] in a
3-dimensional case, and we extend the local method of
computation introduced in [6]. As in [7] we use here
the classification of twisted (stable) regular
conjugacy classes in GL(4, F) of [4], motivated by
Weissauer [13].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baoulina:2006:EFF,
author = "Ioulia Baoulina",
title = "On the Equation Over a Finite Field",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "351--363",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000607",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000607",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hbaib:2006:BDC,
author = "M. Hbaib and M. Mkaouar",
title = "Sur le b{\^e}ta-d{\'e}veloppement de $1$ dans le corps
des s{\'e}ries formelles. ({French}) [{On} the
beta-development of $1$ in the body of formal series]",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "365--378",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000619",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000619",
abstract = "Let \beta be a fixed element of {$ \mathbb {F} $}$_q$
((X$^{-1}$)) with polynomial part of degree \geq 1,
then any formal power series can be represented in base
\beta, using the transformation T$_{\beta }$: f \mapsto
{\beta f} of the unit disk. Any formal power series in
is expanded in this way into d$_{\beta }$ (f) = (a$_i$
(X))$_{i \geq 1}$, where. The main aim of this paper is
to characterize the formal power series \beta (|\beta |
> 1), such that d$_{\beta }$ (1) is finite, eventually
periodic or automatic (such characterizations do not
exist in the real case).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Lev:2006:CPA,
author = "Vsevolod F. Lev",
title = "Critical Pairs in {Abelian} Groups and {Kemperman}'s
Structure Theorem",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "379--396",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000620",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000620",
abstract = "A well-known result by Kemperman describes the
structure of those pairs (A, B) of finite subsets of an
abelian group satisfying |A + B| \leq |A| + |B| -1. We
establish a description which is, in a sense, dual to
Kemperman's, and as an application sharpen several
results due to Deshouillers, Hamidoune, Hennecart, and
Plagne.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Movasati:2006:HSH,
author = "H. Movasati and S. Reiter",
title = "Hypergeometric Series and {Hodge} Cycles of Four
Dimensional Cubic Hypersurfaces",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "397--416",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000632",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000632",
abstract = "In this article we find connections between the values
of Gauss hypergeometric functions and the dimension of
the vector space of Hodge cycles of four-dimensional
cubic hypersurfaces. Since the Hodge conjecture is
well-known for those varieties we calculate values of
hypergeometric series on certain CM points. Our methods
are based on the calculation of the Picard--Fuchs
equations in higher dimensions, reducing them to the
Gauss equation and then applying the Abelian Subvariety
Theorem to the corresponding hypergeometric abelian
varieties.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Matala-Aho:2006:VCF,
author = "Tapani Matala-Aho and Ville Meril{\"a}",
title = "On the values of continued fractions: $q$-series
{II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "417--430",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000656",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000656",
abstract = "Let polynomials $ S(t) $, $ T(t) $ be given, then the
convergence of the $q$-continued fraction $ T(t) +
\mathbb {K}_{n = 1}^\infty \frac {S(t q^{n - 1})}{T(t
q^n)}$ will be studied using the Poincar{\'e}--Perron
Theorem and Frobenius series solutions of the
corresponding q-difference equation $ S(t) H(q^2 t) =
T(t) H(q t) + H(t)$. Our applications include a
generalization of a $q$-continued fraction identity of
Ramanujan and certain $q$-fractions, which arise in the
theory of $q$-orthogonal polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dodson:2006:KTT,
author = "M. M. Dodson and S. Kristensen",
title = "{Khintchine}'s Theorem and Transference Principle for
Star Bodies",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "431--453",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000668",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000668",
abstract = "Analogues of Khintchine's Theorem in simultaneous
Diophantine approximation in the plane are proved with
the classical height replaced by fairly general planar
distance functions or equivalently star bodies.
Khintchine's transference principle is discussed for
distance functions and a direct proof for the
multiplicative version is given. A transference
principle is also established for a different distance
function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rodseth:2006:PPF,
author = "{\O}ystein J. R{\o}dseth and James A. Sellers",
title = "Partitions with Parts in a Finite Set",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "3",
pages = "455--468",
month = sep,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000644",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:14 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000644",
abstract = "For a finite set A of positive integers, we study the
partition function p$_A$ (n). This function enumerates
the partitions of the positive integer n into parts in
A. We give simple proofs of some known and unknown
identities and congruences for p$_A$ (n). For n in a
special residue class, p$_A$ (n) is a polynomial in n.
We examine these polynomials for linear factors, and
the results are applied to a restricted m-ary partition
function. We extend the domain of p$_A$ and prove a
reciprocity formula with supplement. In closing we
consider an asymptotic formula for p$_A$ (n) and its
refinement.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nicolas:2006:VIF,
author = "Jean-Louis Nicolas",
title = "Valeurs impaires de la fonction de partition $ p(n) $.
({French}) [{Odd} values of the partition function $
p(n) $]",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "469--487",
month = dec,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1142/S179304210600067X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210600067X",
abstract = "Let p(n) denote the number of partitions of n, and for
i = 0 (resp. 1), A$_i$ (x) denote the number of n \leq
x such that p(n) is even (resp. odd). In this paper, it
is proved that for some constant K > 0, holds for x
large enough. This estimation slightly improves a
preceding result of S. Ahlgren who obtained the above
lower bound for K = 0. Let and ; the main tool is a
result of J.-P. Serre about the distribution of odd
values of \tau$_k$ (n). Effective lower bounds for
A$_0$ (x) and A$_1$ (x) are also given.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Ayuso:2006:NST,
author = "Pedro Fortuny Ayuso and Fritz Schweiger",
title = "A New Symmetric Two-Dimensional Algorithm",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "489--498",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000681",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000681",
abstract = "Continued fractions are deeply related to Singularity
Theory, as the computation of the Puiseux exponents of
a plane curve from its dual graph clearly shows.
Another closely related topic is Euclid's Algorithm for
computing the gcd of two integers (see [2] for a
detailed overview). In the first section, we describe a
subtractive algorithm for computing the gcd of n
integers, related to singularities of curves in affine
n-space. This gives rise to a multidimensional
continued fraction algorithm whose version in dimension
2 is the main topic of the paper.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cooper:2006:RBP,
author = "Joshua N. Cooper and Dennis Eichhorn and Kevin
O'Bryant",
title = "Reciprocals of Binary Power Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "499--522",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000693",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000693",
abstract = "If A is a set of nonnegative integers containing 0,
then there is a unique nonempty set B of nonnegative
integers such that every positive integer can be
written in the form a + b, where a \in A and b \in B,
in an even number of ways. We compute the natural
density of B for several specific sets A, including the
Prouhet--Thue--Morse sequence, {0} \cup {2$^n$ :n \in
\mathbb{N} }, and random sets, and we also study the
distribution of densities of B for finite sets A. This
problem is motivated by Euler's observation that if A
is the set of n that has an odd number of partitions,
then B is the set of pentagonal numbers {n(3n + 1)/2:n
\in {\mathbb{Z}}}. We also elaborate the connection
between this problem and the theory of de Bruijn
sequences and linear shift registers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bowman:2006:CF,
author = "D. Bowman and J. McLaughlin and N. J. Wyshinski",
title = "A $q$-continued fraction",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "523--547",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S179304210600070X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210600070X",
abstract = "We use the method of generating functions to find the
limit of a q-continued fraction, with 4 parameters, as
a ratio of certain $q$-series. We then use this result
to give new proofs of several known continued fraction
identities, including Ramanujan's continued fraction
expansions for (q$^2$; q$^3$)$_{\infty }$ /(q;
q$^3$)$_{\infty }$ and. In addition, we give a new
proof of the famous Rogers--Ramanujan identities. We
also use our main result to derive two generalizations
of another continued fraction due to Ramanujan.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gun:2006:TZC,
author = "Sanoli Gun",
title = "Transcendental Zeros of Certain Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "549--553",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000711",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000711",
abstract = "Kohnen showed that the zeros of the Eisenstein series
E$_k$ in the standard fundamental domain other than i
and \rho are transcendental. In this paper, we obtain
similar results for a more general class of modular
forms, using the earlier works of Kanou, Kohnen and the
recent work of Getz.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pontreau:2006:GLB,
author = "Corentin Pontreau",
title = "Geometric Lower Bounds for the Normalized Height of
Hypersurfaces",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "555--568",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000723",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000723",
abstract = "Here we are concerned on Bogomolov's problem for
hypersurfaces; we give a geometric lower bound for the
height of a hypersurface of (i.e. without condition on
the field of definition of the hypersurface) which is
not a translate of an algebraic subgroup of . This is
an analogue of a result of F. Amoroso and S. David who
give a lower bound for the height of non-torsion
hypersurfaces defined and irreducible over the
rationals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jadrijevic:2006:SRP,
author = "Borka Jadrijevi{\'c} and Volker Ziegler",
title = "A System of Relative {Pellian} Equations and a Related
Family of Relative {Thue} Equations",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "569--590",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000735",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000735",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Byard:2006:QRD,
author = "Kevin Byard",
title = "On Qualified Residue Difference Sets",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "591--597",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000747",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000747",
abstract = "Qualified residue difference sets of power n are known
to exist for n = 2,4,6, as do similar sets that include
the zero element. Both classes of sets are proved
non-existent for n = 8.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kanemitsu:2006:SNT,
author = "Shigeru Kanemitsu and Yoshio Tanigawa and Haruo
Tsukada",
title = "Some Number Theoretic Applications of a General
Modular Relation",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "599--615",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000759",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000759",
abstract = "We state a form of the modular relation in which the
functional equation appears in the form of an
expression of one Dirichlet series in terms of the
other multiplied by the quotient of gamma functions and
illustrate it by some concrete examples including the
results of Koshlyakov, Berndt and Wigert and Bellman.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2006:AIV,
author = "Anonymous",
title = "Author Index (Volume 2)",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "4",
pages = "617--619",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000760",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042106000760",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Granville:2007:PDP,
author = "Andrew Granville",
title = "Prime Divisors Are {Poisson} Distributed",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "1--18",
month = mar,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042107000778",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See erratum \cite{Granville:2007:EPD}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000778",
abstract = "We show that the set of prime factors of almost all
integers are ``Poisson distributed'', and that this
remains true (appropriately formulated) even when we
restrict the number of prime factors of the integer.
Our results have inspired analogous results about the
distribution of cycle lengths of permutations.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Angles:2007:RI,
author = "Bruno Angl{\`e}s and Thomas Herreng",
title = "On a Result of {Iwasawa}",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "19--41",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000791",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000791",
abstract = "We recover a result of Iwasawa on the $p$-adic
logarithm of principal units of {$ \mathbb
{Q}_p(\zeta_{p^{n + 1}})$} by studying the value at s =
1 of $p$-adic {$L$}-functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Garvan:2007:SSP,
author = "Frank G. Garvan and Hamza Yesilyurt",
title = "Shifted and Shiftless Partition Identities {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "43--84",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000808",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000808",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dilcher:2007:PAS,
author = "Karl Dilcher and Kenneth B. Stolarsky",
title = "A Polynomial Analogue to the {Stern} Sequence",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "85--103",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S179304210700081X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210700081X",
abstract = "We extend the Stern sequence, sometimes also called
Stern's diatomic sequence, to polynomials with
coefficients 0 and 1 and derive various properties,
including a generating function. A simple iteration for
quotients of consecutive terms of the Stern sequence,
recently obtained by Moshe Newman, is extended to this
polynomial sequence. Finally we establish connections
with Stirling numbers and Chebyshev polynomials,
extending some results of Carlitz. In the process we
also obtain some new results and new proofs for the
classical Stern sequence.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Choi:2007:CSP,
author = "H. Timothy Choi and Ronald Evans",
title = "Congruences for Sums of Powers of {Kloosterman} Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "105--117",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000821",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000821",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Shevelev:2007:D,
author = "Vladimir Shevelev",
title = "On divisibility of $ \binom {n - i - 1}{i - 1} $ by
$i$",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "119--139",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S179304210700078X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210700078X",
abstract = "We investigate the function b(n) = \sum 1, where the
summing is over all i for which.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hart:2007:NCM,
author = "William B. Hart",
title = "A New Class of Modular Equation for {Weber}
Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "141--157",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000845",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000845",
abstract = "We describe the construction of a new type of modular
equation for Weber functions. These bear some
relationship to Weber's modular equations of the {\em
irrational kind}. Numerous examples of these
equations are explicitly computed. We also obtain some
modular equations of the irrational kind which are not
present in Weber's work.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Croot:2007:SNS,
author = "Ernie Croot",
title = "Smooth Numbers in Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "1",
pages = "159--169",
month = mar,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000833",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000833",
abstract = "We show that for any \in > 0, there exists c > 0, such
that for all x sufficiently large, there are x$^{1 /
2}$ (log x)$^{-log 4 - o(1)}$ integers, all of whose
prime factors are.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wittmann:2007:PDC,
author = "Christian Wittmann",
title = "$l$-parts of divisor class groups of cyclic function
fields of degree $l$",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "171--190",
month = jun,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042107000857",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000857",
abstract = "Let l be a prime number and K be a cyclic extension of
degree l of the rational function field {$ \mathbb {F}
$}$_q$ (T) over a finite field of characteristic \neq =
l. Using class field theory we investigate the l-part
of Pic$^0$ (K), the group of divisor classes of degree
0 of K, considered as a Galois module. In particular we
give deterministic algorithms that allow the
computation of the so-called (\sigma - 1)-rank and the
(\sigma - 1)$^2$-rank of Pic$^0$ (K), where \sigma
denotes a generator of the Galois group of K/{$ \mathbb
{F} $}$_q$ (T). In the case l = 2 this yields the exact
structure of the 2-torsion and the 4-torsion of Pic$^0$
(K) for a hyperelliptic function field K (and hence of
the {$ \mathbb {F} $}$_q$-rational points on the
Jacobian of the corresponding hyperelliptic curve over
{$ \mathbb {F} $}$_q$). In addition we develop similar
results for l-parts of S-class groups, where S is a
finite set of places of K. In many cases we are able to
prove that our algorithms run in polynomial time.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sole:2007:MFC,
author = "Patrick Sol{\'e} and Dmitrii Zinoviev",
title = "A {Macwilliams} Formula for Convolutional Codes",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "191--206",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000869",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000869",
abstract = "Regarding convolutional codes as polynomial analogues
of arithmetic lattices, we derive a Poisson--Jacobi
formula for their trivariate weight enumerator. The
proof is based on harmonic analysis on locally compact
abelian groups as developed in Tate's thesis to derive
the functional equation of the zeta function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alkan:2007:ASG,
author = "Emre Alkan",
title = "Average Size of Gaps in the {Fourier} Expansion of
Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "207--215",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000870",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000870",
abstract = "We prove that certain powers of the gap function for
the newform associated to an elliptic curve without
complex multiplication are ``finite'' on average. In
particular we obtain quantitative results on the number
of large values of the gap function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Amoroso:2007:MPE,
author = "Francesco Amoroso",
title = "Une minoration pour l'exposant du groupe des classes
d'un corps engendr{\'e} par un nombre de {Salem}.
({French}) [{A} lower bound for the exponent of the
group of classes of a field generated by a number of
{Salem}]",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "217--229",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000882",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000882",
abstract = "In this article we extend the main result of [2]
concerning lower bounds for the exponent of the class
group of CM-fields. We consider a number field K
generated by a Salem number \alpha. If k denotes the
field fixed by \alpha \mapsto \alpha$^{-1}$ we prove,
under the generalized Riemann hypothesis for the
Dedekind zeta function of K, lower bounds for the
relative exponent e$_{K / k}$ and the relative size
h$_{K / k}$ of the class group of K with respect to the
class group of k.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Royer:2007:ECS,
author = "Emmanuel Royer",
title = "Evaluating Convolution Sums of the Divisor Function by
Quasimodular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "231--261",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000924",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000924",
abstract = "We provide a systematic method to compute arithmetic
sums including some previously computed by Alaca,
Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi,
Ou, Ramanujan, Spearman and Williams. Our method is
based on quasimodular forms. This extension of modular
forms has been constructed by Kaneko and Zagier.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mukhopadhyay:2007:ZDE,
author = "Anirban Mukhopadhyay and Kotyada Srinivas",
title = "A Zero Density Estimate for the {Selberg} Class",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "263--273",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000894",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000894",
abstract = "It is well known that bounds on moments of a specific
{$L$}-function can lead to zero-density result for that
{$L$}-function. In this paper, we generalize this
argument to all {$L$}-functions in the Selberg class by
assuming a certain second power moment. As an
application, it is shown that in the case of
symmetric-square {$L$}-function, this result improves
the existing one.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{VanWamelen:2007:NEM,
author = "Paul {Van Wamelen}",
title = "New Explicit Multiplicative Relations Between {Gauss}
Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "275--292",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000900",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000900",
abstract = "We study multiplicative identities between Gauss sums.
If such an identity does not follow from the
Davenport--Hasse relation and the norm relation, it is
called a sign ambiguity. Until recently only a finite
number of explicit sign ambiguities were known. We
generalize the first infinite family of sign
ambiguities as found by Murray.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sills:2007:IRR,
author = "Andrew V. Sills",
title = "Identities of the {Rogers--Ramanujan--Slater} Type",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "2",
pages = "293--323",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000912",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:15 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000912",
abstract = "It is shown that (two-variable generalizations of)
more than half of Slater's list of 130
Rogers--Ramanujan identities (L. J. Slater, Further
identities of the Rogers--Ramanujan type, {\em Proc.
London Math Soc. (2)\/} 54 (1952) 147--167) can be
easily derived using just three multiparameter Bailey
pairs and their associated q-difference equations. As a
bonus, new Rogers--Ramanujan type identities are found
along with natural combinatorial interpretations for
many of these identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2007:P,
author = "Anonymous",
title = "Preface",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "v--vi",
month = sep,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042107001061",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001061",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Andrews:2007:FD,
author = "George E. Andrews",
title = "A {Fine} Dream",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "325--334",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000948",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000948",
abstract = "We shall develop further N. J. Fine's theory of three
parameter non-homogeneous first order q-difference
equations. The object of our work is to bring the
Rogers--Ramanujan identities within the purview of such
a theory. In addition, we provide a number of new
identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{DeAzevedoPribitkin:2007:UPS,
author = "Wladimir {De Azevedo Pribitkin}",
title = "Uninhibited {Poincar{\'e}} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "335--347",
month = sep,
year = "2007",
DOI = "",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210700095X",
abstract = "We introduce a class of functions that generalize the
epoch-making series of Poincar{\'e} and Petersson. Our
``uninhibited Poincar{\'e} series'' permits both a
complex weight and an arbitrary multiplier system that
is independent of the weight. In this initial paper we
provide their Fourier expansions, as well as their
modular behavior. We show that they are modular
integrals that possess interesting periods. Moreover,
we establish with relative ease that they ``almost
never'' vanish identically. Along the way we present a
seemingly unknown historical truth concerning
Kloosterman sums, and also an alternative approach to
Petersson's factor systems. The latter depends upon a
simple multiplication rule.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Berndt:2007:RCP,
author = "Bruce C. Berndt",
title = "{Ramanujan}'s Congruences for the Partition Function
Modulo $5$, $7$, and $ 11$",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "349--354",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000961",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000961",
abstract = "Using Ramanujan's differential equations for
Eisenstein series and an idea from Ramanujan's
unpublished manuscript on the partition function p(n)
and the tau function \tau (n), we provide simple proofs
of Ramanujan's congruences for p(n) modulo 5, 7, and
11.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Iwaniec:2007:FNH,
author = "H. Iwaniec and W. Kohnen and J. Sengupta",
title = "The First Negative {Hecke} Eigenvalue",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "355--363",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001024",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001024",
abstract = "We shall improve earlier estimates on the first sign
change of the Hecke eigenvalues of a normalized
cuspidal newform of level N.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Goldfeld:2007:RLO,
author = "Dorian Goldfeld",
title = "Rank lowering operators on {$ \mathrm {GL}(n, \mathbb
{R}) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "365--375",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000985",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000985",
abstract = "If one takes the Mellin transform of an automorphic
form for GL(n) and then integrates it along the
diagonal on GL(n - 1) then one obtains an automorphic
form on GL(n - 1). This gives a rank lowering operator.
In this paper a more general rank lowering operator is
obtained by combining the Mellin transform with a sum
of powers of certain fixed differential operators. The
analytic continuation of the rank lowering operator is
obtained by showing that the spectral expansion
consists of sums of Rankin--Selberg {$L$}-functions of
type GL(n) $ \times $ GL(n - 1).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mason:2007:VVM,
author = "Geoffrey Mason",
title = "Vector-Valued Modular Forms and Linear Differential
Operators",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "377--390",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000973",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000973",
abstract = "We consider holomorphic vector-valued modular forms F
of integral weight k on the full modular group \Gamma =
SL(2, {\mathbb{Z}}) corresponding to representations of
\Gamma of arbitrary finite dimension p. Assuming that
the component functions of F are linearly independent,
we prove that the inequality k \geq 1 - p always holds,
and that equality holds only in the trivial case when p
= 1 and k = 0. For any p \geq 2, we show how to
construct large numbers of representations of \Gamma
for which k = 2 - p. The key idea is to consider
representations of \Gamma on spaces of solutions of
certain linear differential equations whose
coefficients are modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Caulk:2007:HOH,
author = "Suzanne Caulk and Lynne H. Walling",
title = "{Hecke} Operators on {Hilbert--Siegel} Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "391--420",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001048",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001048",
abstract = "We define Hilbert--Siegel modular forms and Hecke
``operators'' acting on them. As with Hilbert modular
forms (i.e. with Siegel degree 1), these linear
transformations are not linear operators until we
consider a direct product of spaces of modular forms
(with varying groups), modulo natural identifications
we can make between certain spaces. With
Hilbert--Siegel forms (i.e. with arbitrary Siegel
degree) we identify several families of natural
identifications between certain spaces of modular
forms. We associate the Fourier coefficients of a form
in our product space to even integral lattices,
independent of basis and choice of coefficient rings.
We then determine the action of the Hecke operators on
these Fourier coefficients, paralleling the result of
Hafner and Walling for Siegel modular forms (where the
number field is the field of rationals).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Schmidt:2007:CLH,
author = "Thomas A. Schmidt and Mark Sheingorn",
title = "Classifying Low Height Geodesics On {$ \Gamma^3
\setminus \mathcal {H} $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "421--438",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001012",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001012",
abstract = "We show that low height-achieving non-simple geodesics
on a low-index cover of the modular surface can be
classified into seven types, according to the topology
of highest arcs. The lowest geodesics of the signature
(0;2,2,2,\infty)-orbifold are the simple closed
geodesics; these are indexed up to isometry by Markoff
triples of positive integers (x, y, z) with x$^2$ +
y$^2$ + z$^2$ = 3xyz, and have heights. Geodesics
considered by Crisp and Moran have heights ; they
conjectured that these heights, which lie in the
``mysterious region'' between 3 and the Hall ray, are
isolated in the Markoff Spectrum. As a step in
resolving this conjecture, we characterize the geometry
on of geodesic arcs with heights strictly between 3 and
6. Of these, one type of geodesic arc cannot realize
the height of any geodesic.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hassen:2007:EZF,
author = "Abdul Hassen and Hieu D. Nguyen",
title = "The Error Zeta Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "439--453",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001000",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001000",
abstract = "This paper investigates a new special function
referred to as the error zeta function. Derived as a
fractional generalization of hypergeometric zeta
functions, the error zeta function is shown to exhibit
many properties analogous to its hypergeometric
counterpart, including its intimate connection to
Bernoulli numbers. These new properties are treated in
detail and used to demonstrate a pre-functional
equation satisfied by this special function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Murty:2007:OVF,
author = "M. Ram Murty and V. Kumar Murty",
title = "Odd Values of {Fourier} Coefficients of Certain
Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "455--470",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001036",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001036",
abstract = "Let f be a normalized Hecke eigenform of weight k \ge
4 on \Gamma$_0$ (N). Let \lambda$_f$ (n) denote the
eigenvalue of the nth Hecke operator acting on f. We
show that the number of n such that \lambda$_f$ (n)
takes a given value coprime to 2, is finite. We also
treat the case of levels 2$^a$ N$_0$ with a arbitrary
and N$_0$ = 1, 3, 5, 15 and 17. We discuss the
relationship of these results to the classical
conjecture of Lang and Trotter.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Choie:2007:RBF,
author = "Y. Choie and Y. Chung",
title = "Representations of Binary Forms by Quaternary Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "471--474",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000997",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000997",
abstract = "In this paper we study a family of quaternary forms
which represent almost all binary forms of a certain
type. The result follows from the representation number
by the genus of ternary forms and a correspondence
among theta series.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Schmidt:2007:LHG,
author = "Thomas A. Schmidt and Mark Sheingorn",
title = "Low Height Geodesics on {$ \Gamma \setminus \mathcal
{H} $}: Height Formulas and Examples",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "3",
pages = "475--501",
month = sep,
year = "2007",
DOI = "https://doi.org/10.1142/S179304210700105X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210700105X",
abstract = "The Markoff spectrum of binary indefinite quadratic
forms can be studied in terms of heights of geodesics
on low-index covers of the modular surface. The lowest
geodesics on are the simple closed geodesics; these are
indexed up to isometry by Markoff triples of positive
integers (x, y, z) with x$^2$ + y$^2$ + z$^2$ = 3xyz,
and have heights. Geodesics considered by Crisp and
Moran have heights ; they conjectured that these
heights, which lie in the ``mysterious region'' between
3 and the Hall ray, are isolated in the Markoff
Spectrum. In our previous work, we classified the low
height-achieving non-simple geodesics of into seven
types according to the topology of highest arcs. Here,
we obtain explicit formulas for the heights of
geodesics of the first three types; the conjecture
holds for approximation by closed geodesics of any of
these types. Explicit examples show that each of the
remaining types is realized.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Eliahou:2007:BMS,
author = "Shalom Eliahou and Michel Kervaire",
title = "Bounds on the Minimal Sumset Size Function in Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "503--511",
month = dec,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042107001085",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001085",
abstract = "In this paper, we give lower and upper bounds for the
minimal size \mu$_G$ (r,s) of the sumset (or product
set) of two finite subsets of given cardinalities r,s
in a group G. Our upper bound holds for solvable
groups, our lower bound for arbitrary groups. The
results are expressed in terms of variants of the
numerical function \kappa$_G$ (r,s), a generalization
of the Hopf--Stiefel function that, as shown in [6],
exactly models \mu$_G$ (r,s) for G abelian.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Evans:2007:RRP,
author = "Ronald Evans and Mark {Van Veen}",
title = "Rational Representations of Primes by Binary Quadratic
Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "513--528",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107000936",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107000936",
abstract = "Let q be a positive squarefree integer. A prime p is
said to be q-admissible if the equation p = u$^2$ +
qv$^2$ has rational solutions u, v. Equivalently, p is
q-admissible if there is a positive integer k such
that, where is the set of norms of algebraic integers
in. Let k(q) denote the smallest positive integer k
such that for all q-admissible primes p. It is shown
that k(q) has subexponential but suprapolynomial growth
in q, as q \rightarrow \infty.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{El-Guindy:2007:LCR,
author = "Ahmad El-Guindy",
title = "Linear Congruences and Relations on Spaces of Cusp
Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "529--539",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001097",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001097",
abstract = "Let p be a prime and let f be any cusp form of level l
\in {2,3,5,7,13} whose weight satisfy a certain
congruence modulo (p-1). Then we exhibit explicit
linear combinations of the coefficients of f that must
be divisible by p. For a normalized Hecke eigenform,
this translates (under mild restrictions) into the pth
coefficient itself being divisible by a prime ideal
above p in the ring generated by the coefficients of f.
This provides many instances of the so-called
non-ordinary primes. We also discuss linear relations
satisfied universally on the space of modular forms of
these levels. These results extend recent work of
Choie, Kohnen and Ono in the level 1 case.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2007:FRR,
author = "Wai Kiu Chan and A. G. Earnest and Maria Ines Icaza
and Ji Young Kim",
title = "Finiteness Results for Regular Definite Ternary
Quadratic Forms Over",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "541--556",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001103",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001103",
abstract = "Let {$ \mathfrak {o} $} be the ring of integers in a
number field. An integral quadratic form over {$
\mathfrak {o} $} is called regular if it represents all
integers in {$ \mathfrak {o} $} that are represented by
its genus. In [13,14] Watson proved that there are only
finitely many inequivalent positive definite primitive
integral regular ternary quadratic forms over
{\mathbb{Z}}. In this paper, we generalize Watson's
result to totally positive regular ternary quadratic
forms over. We also show that the same finiteness
result holds for totally positive definite spinor
regular ternary quadratic forms over, and thus extends
the corresponding finiteness results for spinor regular
quadratic forms over {\mathbb{Z}} obtained in [1,3].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pal:2007:EID,
author = "Ambrus P{\'a}l",
title = "On the {Eisenstein} Ideal of {Drinfeld} Modular
Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "557--598",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001115",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001115",
abstract = "Let {$ \mathfrak {E} $}({$ \mathfrak {p} $}) denote
the Eisenstein ideal in the Hecke algebra {$ \mathbb
{T} $}({$ \mathfrak {p} $}) of the Drinfeld modular
curve X$_0$ ({$ \mathfrak {p} $}) parameterizing
Drinfeld modules of rank two over {$ \mathbb {F} $}$_q$
[T] of general characteristic with Hecke level {$
\mathfrak {p} $}-structure, where {$ \mathfrak {p} $}
\triangleleft {$ \mathbb {F} $}$_q$ [T] is a non-zero
prime ideal. We prove that the characteristic p of the
field {$ \mathbb {F} $}$_q$ does not divide the order
of the quotient {$ \mathbb {T} $}({$ \mathfrak {p}
$})/{$ \mathfrak {E} $}({$ \mathfrak {p} $}) and the
Eisenstein ideal {$ \mathfrak {E} $}({$ \mathfrak {p}
$}) is locally principal.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Moshe:2007:CMR,
author = "Yossi Moshe",
title = "On a Conjecture of {McIntosh} Regarding
{LP}-Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "599--610",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001139",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001139",
abstract = "A sequence over {\mathbb{Z}} is an LP-sequence if for
every prime p and integer n \geq 0 we have (mod p),
when is a base p expansion of n. In this paper, we
study sequences such that both, are LP-sequences for
some d \geq 2. One of those sequences is a
counter-example to a conjecture of McIntosh [15].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kraus:2007:CES,
author = "Alain Kraus",
title = "Courbes elliptiques semi-stables sur les corps de
nombres. ({French}) [{Semi}-stable elliptical curves on
number fields]",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "611--633",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001127",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001127",
abstract = "Let K be a number field. In this paper, we are
interested in the following problem: does there exist a
constant c$_K$, which depends only on K, such that for
any semi-stable elliptic curve defined over K, the
Galois representation in its $p$-torsion points is
irreducible whenever p is a prime number greater than
c$_K$ ? In case the answer is positive, how can we get
such a constant? We prove that if a certain condition
is satisfied by K, the answer is positive and we obtain
c$_K$ explicitly. Furthermore, we prove that this
condition is realized in many situations.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Becheanu:2007:SCD,
author = "Mircea Becheanu and Florian Luca and Igor E.
Shparlinski",
title = "On the Sums of Complementary Divisors",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "635--648",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001152",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001152",
abstract = "In this paper, we study various arithmetic properties
of d + n/d, where d runs through all the \tau (n)
positive divisors of n. For example, denoting by \varpi
(n) the number of prime values among these sums, we
study how often \varpi (n) > 0 and also \varpi (n) =
\tau (n), and we also evaluate the average value of
\varpi (n). We estimate some character sums with d +
n/d and study the distribution of quadratic nonresidues
and primitive roots among these sums on average over n
\leq x.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Granville:2007:EPD,
author = "Andrew Granville",
title = "Erratum: {``Prime Divisors Are Poisson
Distributed''}",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "649--651",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001073",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See \cite{Granville:2007:PDP}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001073",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2007:AIV,
author = "Anonymous",
title = "Author Index (Volume 3)",
journal = j-INT-J-NUMBER-THEORY,
volume = "3",
number = "4",
pages = "653--654",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1142/S1793042107001164",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042107001164",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cooper:2008:CMF,
author = "Yaim Cooper and Nicholas Wage and Irena Wang",
title = "Congruences for Modular Forms of Non-Positive Weight",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "1--13",
month = feb,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042108001171",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001171",
abstract = "In this paper, we consider modular forms f(z) whose
$q$-series expansions \sum b(n)q$^n$ have coefficients
in a localized ring of algebraic integers. Extending
results of Serre and Ono, we show that if f has
non-positive weight, a congruence of the form b(\ell n
+ a) \equiv 0 (mod \nu), where \nu is a place over \ell
in, can hold for only finitely many primes \ell \geq 5.
To obtain this, we establish an effective bound on \ell
in terms of the weight and the structure of f(z).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Takahashi:2008:APM,
author = "S. Takahashi",
title = "$p$-adic periods of modular elliptic curves and the
level-lowering theorem",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "15--23",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001183",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001183",
abstract = "An elliptic curve defined over the field of rational
numbers can be considered as a complex torus. We can
describe its complex periods in terms of integration of
the weight-2 cusp form corresponding to the elliptic
curve. In this paper, we will study an analogous
description of the $p$-adic periods of the elliptic
curve, considering the elliptic curve as a $p$-adic
torus. An essential tool for the proof of such a
description is the level-lowering theorem of Ribet,
which is one of the main ingredients used in the proof
of Fermat's Last Theorem.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bundschuh:2008:ARC,
author = "Peter Bundschuh",
title = "Arithmetical results on certain $q$-series, {I}",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "25--43",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001201",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001201",
abstract = "Entire transcendental solutions of certain mth order
linear q-difference equations with polynomial
coefficients are considered. The aim of this paper is
to give, under appropriate arithmetical conditions,
lower bounds for the dimension of the K-vector space
generated by 1 and the values of these solutions at m
successive powers of q, where K is the rational or an
imaginary quadratic number field. The main ingredients
of the proofs are, first, Nesterenko's dimension
estimate and its various generalizations, and secondly,
Popov's method (in T{\"o}pfer's version) for the
asymptotic evaluation of certain complex integrals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knafo:2008:ELB,
author = "Emmanuel Knafo",
title = "Effective Lower Bound for the Variance of Distribution
of Primes in Arithmetic Progressions",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "45--56",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001213",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001213",
abstract = "Through a refinement for the estimation of the effect
of Siegel zeros, we show how to avoid the use of
Siegel's theorem in order to obtain the first {\em
effective\/} lower bound for the variance of
distribution of primes in arithmetic progressions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dujella:2008:PVP,
author = "Andrej Dujella and Clemens Fuchs and Florian Luca",
title = "A Polynomial Variant of a Problem of {Diophantus} for
Pure Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "57--71",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001225",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001225",
abstract = "In this paper, we prove that there does not exist a
set of 11 polynomials with coefficients in a field of
characteristic 0, not all constant, with the property
that the product of any two distinct elements plus 1 is
a perfect square. Moreover, we prove that there does
not exist a set of 5 polynomials with the property that
the product of any two distinct elements plus 1 is a
perfect kth power with k \geq 7. Combining these
results, we get an absolute upper bound for the size of
a set with the property that the product of any two
elements plus 1 is a pure power.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhao:2008:WTT,
author = "Jianqiang Zhao",
title = "{Wolstenholme} Type Theorem for Multiple Harmonic
Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "73--106",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001146",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001146",
abstract = "In this paper, we will study the $p$-divisibility of
multiple harmonic sums (MHS) which are partial sums of
multiple zeta value series. In particular, we provide
some generalizations of the classical Wolstenholme's
Theorem to both homogeneous and non-homogeneous sums.
We make a few conjectures at the end of the paper and
provide some very convincing evidence.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rath:2008:DC,
author = "P. Rath and K. Srilakshmi and R. Thangadurai",
title = "On {Davenport}'s Constant",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "107--115",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001195",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001195",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kohl:2008:CCT,
author = "Stefan Kohl",
title = "On Conjugates of {Collatz}-Type Mappings",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "117--120",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001237",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001237",
abstract = "A mapping f : {\mathbb{Z}} \rightarrow {\mathbb{Z}} is
called {\em residue-class-wise affine\/} if there is a
positive integer m such that it is affine on residue
classes (mod m). If there is a finite set S \subset
{\mathbb{Z}} which intersects nontrivially with any
trajectory of f, then f is called {\em almost
contracting}. Assume that f is a surjective but not
injective residue-class-wise affine mapping, and that
the preimage of any integer under f is finite. Then f
is almost contracting if and only if there is a
permutation \sigma of {\mathbb{Z}} such that f$^{\sigma
}$ = \sigma$^{-1}$ \odot f \odot \sigma is
either monotonically increasing or monotonically
decreasing almost everywhere. In this paper it is shown
that if there is no positive integer k such that
applying f$^{(k)}$ decreases the absolute value of
almost all integers, then \sigma cannot be
residue-class-wise affine itself. The original
motivation for the investigations in this paper comes
from the famous 3n + 1 Conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Akbary:2008:SCP,
author = "Amir Akbary and Sean Alaric and Qiang Wang",
title = "On Some Classes of Permutation Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "121--133",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001249",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001249",
abstract = "Let p be a prime and q = p$^m$. We investigate
permutation properties of polynomials P(x) = x$^r$ +
x$^{r + s}$ + \cdots + x$^{r + ks}$ (0 < r < q - 1, 0 <
s < q - 1, and k \geq 0) over a finite field {$ \mathbb
{F} $}$_q$. More specifically, we construct several
classes of permutation polynomials of this form over {$
\mathbb {F} $}$_q$. We also count the number of
permutation polynomials in each class.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kirschenhofer:2008:FTT,
author = "P. Kirschenhofer and A. Peth{\H{o}} and J. M.
Thuswaldner",
title = "On a Family of Three Term Nonlinear Integer
Recurrences",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "135--146",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001250",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001250",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Interlando:2008:FAG,
author = "J. Carmelo Interlando and Andr{\'e} Luiz Flores and
Trajano Pires {Da N{\'o}brega Neto}",
title = "A Family of Asymptotically Good Lattices Having a
Lattice in Each Dimension",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "1",
pages = "147--154",
month = feb,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001262",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:16 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001262",
abstract = "A new constructive family of asymptotically good
lattices with respect to sphere packing density is
presented. The family has a lattice in every dimension
n \geq 1. Each lattice is obtained from a conveniently
chosen integral ideal in a subfield of the cyclotomic
field {$ \mathbb {Q} $}(\zeta$_q$) where q is the
smallest prime congruent to 1 modulo n.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sun:2008:LTC,
author = "Zhi-Wei Sun and Daqing Wan",
title = "{Lucas}-type congruences for cyclotomic $ \psi
$-coefficients",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "155--170",
month = apr,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042108001286",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001286",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kazalicki:2008:LRC,
author = "Matija Kazalicki",
title = "Linear Relations for Coefficients of {Drinfeld}
Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "171--176",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001274",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001274",
abstract = "Choie, Kohnen and Ono have recently classified the
linear relations among the initial Fourier coefficients
of weight k modular forms on SL$_2$ ({\mathbb{Z}}), and
they employed these results to obtain particular
$p$-divisibility properties of some $p$-power Fourier
coefficients that are common to all modular forms of
certain weights. Using this, they reproduced some
famous results of Hida on non-ordinary primes. Here we
generalize these results to Drinfeld modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Abouzaid:2008:HLA,
author = "Mourad Abouzaid",
title = "Heights and logarithmic $ \gcd $ on algebraic curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "177--197",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001298",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001298",
abstract = "Let F(x,y) be an irreducible polynomial over {$
\mathbb {Q} $}, satisfying F(0,0) = 0. Skolem proved
that the integral solutions of F(x,y) = 0 with fixed
gcd are bounded [13] and Walsh gave an explicit bound
in terms of d = gcd(x,y) and F [16]. Assuming that
(0,0) is a non-singular point of the plane curve F(x,y)
= 0, we extend this result to algebraic solution, and
obtain an asymptotic equality instead of inequality. We
show that for any algebraic solution (\alpha , \beta),
the quotient h(\alpha)/log d is approximatively equal
to deg$_y$ F and the quotient h(\beta)/log d to deg$_x$
F; here h(\cdotp ) is the absolute logarithmic height
and d is the (properly defined) ``greatest common
divisor'' of \alpha and \beta.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mortenson:2008:BDP,
author = "Eric Mortenson",
title = "On the Broken $1$-Diamond Partition",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "199--218",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001365",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001365",
abstract = "We introduce a crank-like statistic for a different
class of partitions. In [4], Andrews and Paule
initiated the study of broken k-diamond partitions.
Their study of the respective generating functions led
to an infinite family of modular forms, about which
they were able to produce interesting arithmetic
theorems and conjectures for the related partition
functions. Here we establish a crank-like statistic for
the broken 1-diamond partition and discuss its role in
congruence properties.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alaca:2008:TFI,
author = "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Mathieu F.
Lemire and Kenneth S. Williams",
title = "Theta Function Identities and Representations by
Certain Quaternary Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "219--239",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001304",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001304",
abstract = "Some new theta function identities are proved and used
to determine the number of representations of a
positive integer n by certain quaternary quadratic
forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Harman:2008:WMV,
author = "Glyn Harman",
title = "{Watt}'s Mean Value Theorem and {Carmichael} Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "241--248",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001316",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001316",
abstract = "It is shown that Watt's new mean value theorem on sums
of character sums can be included in the method
described in the author's recent work [6] to show that
the number of Carmichael numbers up to x exceeds
x$^{{\u {2}153}}$ for all large x. This is done by
comparing the application of Watt's original version of
his mean value theorem [8] to the problem of primes in
short intervals [3] with the problem of finding
``small'' primes in an arithmetic progression.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Watt:2008:BMV,
author = "Nigel Watt",
title = "Bounds for a Mean Value of Character Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "249--293",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001328",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001328",
abstract = "We obtain new upper bounds for the mean squared
modulus of sums $ \sum_{n \in \mathbb {N} } $ A$_n$
\chi (n), where the sequence (A$_n$) is fixed and the
variable \chi belongs to the set of non-principal
Dirichlet characters for some modulus q. It is assumed
that, for some M, some complex sequence (c$_m$)
satisfying $ c_m = 0$ for $ m \notin (M / 2, M]$, and
some $ \alpha (x)$ and $ \beta (y)$ (smooth functions
with compact support), one has $ A_n = \sum_{u v m = n}
\alpha (u) \beta (v) c_m (n \in \mathbb {N})$. There is
a natural analogy between the bounds obtained and
bounds on mean values of Dirichlet polynomials
previously obtained by Deshouillers and Iwaniec. Our
proofs make use of results from the spectral theory of
automorphic functions, including the bound of Kim and
Sarnak for the eigenvalues of Hecke operators acting on
certain spaces of Maass cusp forms. The results depend
on the size of $P$, the largest prime factor of $q$,
and improve as $ \log_q(P)$ is diminished. In separate
work, Harman has given an application of our results to
the theory of Carmichael numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Penniston:2008:ARP,
author = "David Penniston",
title = "Arithmetic of $ \ell $-regular partition functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "295--302",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001341",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001341",
abstract = "Let b$_{\ell }$ (n) denote the number of \ell -regular
partitions of n, where \ell is prime and 3 \leq \ell
\leq 23. In this paper we prove results on the
distribution of b$_{\ell }$ (n) modulo m for any odd
integer m > 1 with 3 \nmid m if \ell \neq 3.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bringmann:2008:RCO,
author = "Kathrin Bringmann and Jeremy Lovejoy",
title = "Rank and Congruences for Overpartition Pairs",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "303--322",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001353",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001353",
abstract = "The rank of an overpartition pair is a generalization
of Dyson's rank of a partition. The purpose of this
paper is to investigate the role that this statistic
plays in the congruence properties of, the number of
overpartition pairs of n. Some generating functions and
identities involving this rank are also presented.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Milas:2008:NTP,
author = "Antun Milas and Eric Mortenson and Ken Ono",
title = "Number Theoretic Properties of {Wronskians} of
{Andrews--Gordon} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "2",
pages = "323--337",
month = apr,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001377",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001377",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nedev:2008:BSV,
author = "Zhivko Nedev and Anthony Quas",
title = "Balanced Sets and the Vector Game",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "339--347",
month = jun,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1142/S179304210800133X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210800133X",
abstract = "We consider the notion of a balanced set modulo N. A
nonempty set S of residues modulo N is balanced if for
each x \in S, there is a d with 0 < d \leq N/2 such
that x \pm d mod N both lie in S. We define \alpha (N)
to be the minimum cardinality of a balanced set modulo
N. This notion arises in the context of a two-player
game that we introduce and has interesting connections
to the prime factorization of N. We demonstrate that
for p prime, \alpha (p) = \Theta (log p), giving an
explicit algorithmic upper bound and a lower bound
using finite field theory and show that for N
composite, \alpha (N) = min$_{p|N}$ \alpha (p).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Brueggeman:2008:LCD,
author = "Sharon Brueggeman and Darrin Doud",
title = "Local Corrections of Discriminant Bounds and Small
Degree Extensions of Quadratic Base Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "349--361",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001389",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001389",
abstract = "Using analytic techniques of Odlyzko and Poitou, we
create tables of lower bounds for discriminants of
number fields, including local corrections for ideals
of known norm. Comparing the lower bounds found in
these tables with upper bounds on discriminants of
number fields obtained from calculations involving
differents, we prove the nonexistence of a number of
small degree extensions of quadratic fields having
limited ramification. We note that several of our
results require the locally corrected bounds.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bacher:2008:NIH,
author = "Roland Bacher",
title = "A New Inequality for the {Hermite} Constants",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "363--386",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001390",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001390",
abstract = "We describe continuous increasing functions C$_n$ (x)
such that \gamma$_n$ \geq C$_n$ (\gamma$_{n - 1}$)
where \gamma$_m$ is Hermite's constant in dimension m.
This inequality yields a new proof of the
Minkowski--Hlawka bound \Delta$_n$ \geq \zeta (n)2$^{1
- n}$ for the maximal density \Delta$_n$ of
n-dimensional lattice packings.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Coulangeon:2008:EZF,
author = "Renaud Coulangeon",
title = "On {Epstein}'s Zeta Function of {Humbert} Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "387--401",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001407",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001407",
abstract = "The Epstein \zeta function \zeta (\Gamma, s) of a
lattice \Gamma is defined by a series which converges
for any complex number s such that {\mathfrak{R}} s >
n/2, and admits a meromorphic continuation to the
complex plane, with a simple pole at s = n/2. The
question as to which \Gamma, for a fixed s, minimizes
\zeta (\Gamma, s), has a long history, dating back to
Sobolev's work on numerical integration, and subsequent
papers by Delone and Ryshkov among others. This was
also investigated more recently by Sarnak and
Strombergsson. The present paper is concerned with
similar questions for positive definite quadratic forms
over number fields, also called {\em Humbert forms}.
We define Epstein zeta functions in that context and
study their meromorphic continuation and functional
equation, this being known in principle but somewhat
hard to find in the literature. Then, we give a general
criterion for a Humbert form to be {\em finally\/}
\zeta {\em extreme\/}, which we apply to a family of
examples in the last section.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Matsuno:2008:AII,
author = "Kazuo Matsuno",
title = "On the $2$-Adic {Iwasawa} Invariants of Ordinary
Elliptic Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "403--422",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001468",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001468",
abstract = "In this paper, we give an explicit formula describing
the variation of the 2-adic Iwasawa \lambda -invariants
attached to the Selmer groups of elliptic curves under
quadratic twists. To prove this formula, we extend some
results known for odd primes p, an analogue of Kida's
formula proved by Hachimori and the author and a
formula given by Greenberg and Vatsal, to the case
where p = 2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lau:2008:LQN,
author = "Yuk-Kam Lau and Jie Wu",
title = "On the Least Quadratic Non-Residue",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "423--435",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001432",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001432",
abstract = "We prove that for almost all real primitive characters
\chi$_d$ of modulus |d|, the least positive integer
n$_{\chi d}$ at which \chi$_d$ takes a value not equal
to 0 and 1 satisfies n$_{\chi d}$ \ll log|d|, and give
a quite precise estimate on the size of the exceptional
set.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ong:2008:EET,
author = "Yao Lin Ong and Minking Eie and Wen-Chin Liaw",
title = "Explicit Evaluation of Triple {Euler} Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "437--451",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001420",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001420",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kochubei:2008:DCE,
author = "Anatoly N. Kochubei",
title = "{Dwork--Carlitz} Exponential and Overconvergence for
Additive Functions in Positive Characteristic",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "453--460",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001444",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001444",
abstract = "We study overconvergence phenomena for {$ \mathbb {F}
$}-linear functions on a function field over a finite
field {$ \mathbb {F} $}. In particular, an analog of
the Dwork exponential is introduced.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Toh:2008:GTO,
author = "Pee Choon Toh",
title = "Generalized $m$-th order {Jacobi} theta functions and
the {Macdonaldcg} identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "461--474",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001456",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001456",
abstract = "We describe an mth order generalization of Jacobi's
theta functions and use these functions to construct
classes of theta function identities in multiple
variables. These identities are equivalent to the
Macdonald identities for the seven infinite families of
irreducible affine root systems. They are also
equivalent to some elliptic determinant evaluations
proven recently by Rosengren and Schlosser.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sankaranarayanan:2008:ESC,
author = "A. Sankaranarayanan and N. Saradha",
title = "Estimates for the Solutions of Certain {Diophantine}
Equations by {Runge}'s Method",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "475--493",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S179304210800147X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210800147X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhang:2008:ACS,
author = "Lingrui Zhang and Qin Yue",
title = "Another Case of a {Scholz}'s Theorem on Class Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "495--501",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001493",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001493",
abstract = "In this paper, we give necessary and sufficient
conditions for 8-ranks of narrow class groups of,
distinct primes p \equiv q \equiv 1 mod 4. The results
are useful for numerical computations.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fukshansky:2008:SZQ,
author = "Lenny Fukshansky",
title = "Small Zeros of Quadratic Forms Over",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "3",
pages = "503--523",
month = jun,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001481",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001481",
abstract = "Let N \geq 2 be an integer, F a quadratic form in N
variables over, and an $L$-dimensional subspace, 1 \leq
L \leq N. We prove the existence of a small-height
maximal totally isotropic subspace of the bilinear
space (Z,F). This provides an analogue over of a
well-known theorem of Vaaler proved over number fields.
We use our result to prove an effective version of Witt
decomposition for a bilinear space over. We also
include some related effective results on orthogonal
decomposition and structure of isometries for a
bilinear space over. This extends previous results of
the author over number fields. All bounds on height are
explicit.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baruah:2008:SSS,
author = "Nayandeep Deka Baruah and Shaun Cooper and Michael
Hirschhorn",
title = "Sums of Squares and Sums of Triangular Numbers Induced
by Partitions of $8$",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "525--538",
month = aug,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1142/S179304210800150X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210800150X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chapman:2008:AWT,
author = "Robin Chapman and Hao Pan",
title = "$q$-analogues of {Wilson}'s theorem",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "539--547",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001511",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001511",
abstract = "We give q-analogues of Wilson's theorem for the primes
congruent to 1 and 3 modulo 4, respectively. Also
q-analogues of two congruences due to Mordell and
Chowla are established.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Schwab:2008:UFC,
author = "Emil Daniel Schwab and Pentti Haukkanen",
title = "A unique factorization in commutative {M{\"o}bius}
monoids",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "549--561",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001523",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001523",
abstract = "We show that any commutative M{\"o}bius monoid
satisfies a unique factorization theorem and thus
possesses arithmetical properties similar to those of
the multiplicative semigroup of positive integers.
Particular attention is paid to standard examples,
which arise from the bicyclic semigroup and the
multiplicative analogue of the bicyclic semigroup. The
second example shows that the Fundamental Theorem of
Arithmetic is a special case of the unique
factorization theorem in commutative M{\"o}bius
monoids. As an application, we study generalized
arithmetical functions defined on an arbitrary
commutative M{\"o}bius monoid.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Oura:2008:TSR,
author = "Manabu Oura and Cris Poor and David S. Yuen",
title = "Towards the {Siegel} Ring in Genus Four",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "563--586",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001535",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001535",
abstract = "Runge gave the ring of genus three Siegel modular
forms as a quotient ring, R$_3$ /{\u{3}008}J$^{(3)}$
{\u{3}009} where R$_3$ is the genus three ring of code
polynomials and J$^{(3)}$ is the difference of the
weight enumerators for the e$_8$ \oplus e$_8$ and
codes. Freitag and Oura gave a degree 24 relation,, of
the corresponding ideal in genus four; where is also a
linear combination of weight enumerators. We take
another step towards the ring of Siegel modular forms
in genus four. We explain new techniques for computing
with Siegel modular forms and actually compute six new
relations, classifying all relations through degree 32.
We show that the local codimension of any irreducible
component defined by these known relations is at least
3 and that the true ideal of relations in genus four is
not a complete intersection. Also, we explain how to
generate an infinite set of relations by symmetrizing
first order theta identities and give one example in
degree 32. We give the generating function of R$_5$ and
use it to reprove results of Nebe [25] and Salvati
Manni [37].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bonciocat:2008:CLP,
author = "Nicolae Ciprian Bonciocat",
title = "Congruences and {Lehmer}'s Problem",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "587--596",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001547",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001547",
abstract = "We obtain explicit lower bounds for the Mahler measure
for nonreciprocal polynomials with integer coefficients
satisfying certain congruences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chakraborty:2008:ECG,
author = "Kalyan Chakraborty and Florian Luca and Anirban
Mukhopadhyay",
title = "Exponents of Class Groups of Real Quadratic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "597--611",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001559",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001559",
abstract = "In this paper, we show that the number of real
quadratic fields {$ \mathbb {K} $} of discriminant $
\Delta_{ \mathbb {K}} < x $ whose class group has an
element of order $g$ (with $g$ even) is $ \geq x^{1 /
g} / 5 $ if $ x > x_0 $, uniformly for positive
integers $ g \leq (\log \log x) / (8 \log \log \log x)
$. We also apply the result to find real quadratic
number fields whose class numbers have many prime
factors.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Masri:2008:IFF,
author = "Nadia Masri",
title = "Infinite Families of Formulas for Sums of Integer
Squares",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "613--626",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001560",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001560",
abstract = "In 2002, Milne [5, 6] obtained ten infinite families
of formulas for the sums of integer squares. Recently,
Long and Yang [4] reproved four of these identities
using modular forms on various subgroups. In this
paper, we prove the remaining six, and show that all of
the identities can be proved by interpreting them in
terms of modular forms for \Gamma$_0$ (4).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Clark:2008:AHP,
author = "Pete L. Clark",
title = "An ``anti-{Hasse} Principle'' for Prime Twists",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "627--637",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001572",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001572",
abstract = "Given an algebraic curve $ C_{\mathbb {Q}} $ having
points everywhere locally and endowed with a suitable
involution, we show that there exists a positive
density family of prime quadratic twists of C violating
the Hasse principle. The result applies in particular
to $ w_N$-Atkin--Lehner twists of most modular curves
X$_0 (N)$ and to $ w_p$-Atkin--Lehner twists of certain
Shimura curves $ X^{D+}$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pineda-Ruelas:2008:EGG,
author = "Mario Pineda-Ruelas and Gabriel D. Villa-Salvador",
title = "Explicit {Galois} Group Realizations",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "639--652",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001584",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001584",
abstract = "We study the embedding problem with abelian kernel and
we obtain a homogeneous system of equations, which
leads directly to the explicit realization of a finite
group with certain properties. We give an example
motivated by finding explicitly nonsolitary fields of
degree 18 over {$ \mathbb {Q} $}.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Farag:2008:DTR,
author = "Hany M. Farag",
title = "{Dirichlet} Truncations of the {Riemann} Zeta Function
in the Critical Strip Possess Zeros Near Every Vertical
Line",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "653--662",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001596",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001596",
abstract = "We study the zeros of the finite truncations of the
alternating Dirichlet series expansion of the Riemann
zeta function in the critical strip. We do this with an
(admittedly highly) ambitious goal in mind. Namely,
that this series converges to the zeta function (up to
a trivial term) in the critical strip and our hope is
that if we can obtain good estimates for the zeros of
these approximations it may be possible to generalize
some of the results to zeta itself. This paper is a
first step towards this goal. Our results show that
these finite approximations have zeros near every
vertical line (so no vertical strip in this region is
zero-free). Furthermore, we give upper bounds for the
imaginary parts of the zeros (the real parts are
pinned). The bounds are numerically very large. Our
tools are: the inverse mapping theorem (for a
perturbative argument), the prime number theorem (for
counting primes), elementary geometry (for constructing
zeros of a related series), and a quantitative version
of Kronecker's theorem to go from one series to
another.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ash:2008:EUA,
author = "Avner Ash and David Pollack",
title = "Everywhere unramified automorphic cohomology for {$
\mathrm {SL}_3 (\mathbb {Z}) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "663--675",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001602",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001602",
abstract = "We conjecture that the only irreducible cuspidal
automorphic representations for GL$_3$ /{$ \mathbb
{Q}$} of cohomological type and level 1 are (up to
twisting) the symmetric square lifts of classical
cuspforms on GL$_2$ /{$ \mathbb {Q}$} of level 1. We
present computational evidence for this conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alaca:2008:BCF,
author = "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Kenneth S.
Williams",
title = "{Berndt}'s Curious Formula",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "677--689",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001614",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001614",
abstract = "A curious arithmetic formula deduced by Berndt from an
analytic formula of Ramanujan is proved arithmetically
and used to prove the formulae given by Liouville for
the number of representations of a positive integer by
the forms $ x^2 + y^2 + z^2 + t^2 + 2 u^2 + 2 v^2 $ and
$ x^2 + y^2 + 2 z^2 + 2 t^2 + 2 u^2 + 2 v^2 $.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Boca:2008:PES,
author = "Florin P. Boca",
title = "A problem of {Erd{\H{o}}s}, {Sz{\"o}sz} and
{Tur{\'a}n} concerning {Diophantine} approximations",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "4",
pages = "691--708",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001626",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:17 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001626",
abstract = "For $ A > 0 $ and $ c > 1 $, let $ S(N, A, c) $ denote
the set of those numbers $ \theta \in ]0, 1 [ $ which
satisfy for some coprime integers $a$ and $b$ with $ N
< b \leq c N$. The problem of the existence and
computation of the limit $ f(A, c)$ of the Lebesgue
measure of $ S(N, A, c)$ as $ N \to \infty $ was raised
by Erd{\H{o}}s, Sz{\"u}sz and Tur{\'a}n [3]. This limit
has been shown to exist by Kesten and S{\'o}s [5] using
a probabilistic argument and explicitly computed when $
A c \leq 1$ by Kesten [4]. We give a complete solution
proving directly the existence of this limit and
identifying it in all cases.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chapman:2008:RIF,
author = "Robin Chapman",
title = "Representations of integers by the form $ x^2 + x y +
y^2 + z^2 + z t + t^2 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "709--714",
month = oct,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042108001638",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001638",
abstract = "We give an elementary proof of the number of
representations of an integer by the quaternary
quadratic form x$^2$ + xy + y$^2$ + z$^2$ + zt +
t$^2$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Languasco:2008:HLP,
author = "Alessandro Languasco and Alessandro Zaccagnini",
title = "On the {Hardy--Littlewood} Problem in Short
Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "715--723",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S179304210800164X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210800164X",
abstract = "We study the distribution of Hardy--Littlewood numbers
in short intervals both unconditionally and
conditionally, i.e. assuming the Riemann Hypothesis
(RH). We prove that a suitable average of the
asymptotic formula for the number of representations of
a Hardy--Littlewood number holds in the interval [n, n
+ H], where H < X$^{1 - 1 / k + \in }$ and n \in [X,
2X].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kopeliovich:2008:TCI,
author = "Yaacov Kopeliovich",
title = "Theta Constant Identities at Periods of Coverings of
Degree 3",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "725--733",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001663",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001663",
abstract = "We derive relations between theta functions evaluated
at period matrices of cyclic covers of order 3 ramified
above 3k points.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mizuno:2008:ALS,
author = "Yoshinori Mizuno",
title = "A $p$-adic limit of {Siegel--Eisenstein} series of
prime level $q$",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "735--746",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001729",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001729",
abstract = "We show that a $p$-adic limit of a Siegel--Eisenstein
series of prime level q becomes a Siegel modular form
of level pq. This paper contains a simple formula for
Fourier coefficients of a Siegel--Eisenstein series of
degree two and prime levels.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ernvall-Hytonen:2008:ETA,
author = "Anne-Maria Ernvall-Hyt{\"o}nen",
title = "On the Error Term in the Approximate Functional
Equation for Exponential Sums Related to Cusp Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "747--756",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001730",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001730",
abstract = "We give a proof for the approximate functional
equation for exponential sums related to holomorphic
cusp forms and derive an upper bound for the error
term.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Thunder:2008:PBH,
author = "Jeffrey Lin Thunder",
title = "Points of Bounded Height on {Schubert} Varieties",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "757--765",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001742",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001742",
abstract = "Growth estimates and asymptotic estimates are given
for the number of rational points of bounded height on
Schubert varieties defined over number fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hassen:2008:HBP,
author = "Abdul Hassen and Hieu D. Nguyen",
title = "Hypergeometric {Bernoulli} Polynomials and {Appell}
Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "767--774",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001754",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001754",
abstract = "There are two analytic approaches to Bernoulli
polynomials B$_n$ (x): either by way of the generating
function ze$^{xz}$ /(e$^z$- 1) = \sum B$_n$ (x)z$^n$
/n! or as an Appell sequence with zero mean. In this
article, we discuss a generalization of Bernoulli
polynomials defined by the generating function z$^N$
e$^{xz}$ /(e$^z$- T$_{N - 1}$ (z)), where T$_N$ (z)
denotes the Nth Maclaurin polynomial of e$^z$, and
establish an equivalent definition in terms of Appell
sequences with zero moments in complete analogy to
their classical counterpart. The zero-moment condition
is further shown to generalize to Bernoulli polynomials
generated by the confluent hypergeometric series.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Onodera:2008:BSG,
author = "Kazuhiro Onodera",
title = "Behavior of Some Generalized Multiple Sine Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "775--796",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001651",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001651",
abstract = "Our aim is to investigate the behavior of generalized
multiple sine functions with general period parameters
in the fundamental domain. For that, we need to
calculate the number of their extremal values. By
estimating their special values, we determine it in
some cases including the quintuple sine function. As a
consequence, we sketch their graphs.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baoulina:2008:NSE,
author = "Ioulia Baoulina",
title = "On the number of solutions to the equation $ (x_1 +
\cdots + x_n)^2 = a x_1 \cdots x_n $ in a finite
field",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "797--817",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001675",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001675",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ford:2008:CFF,
author = "Kevin Ford and Igor Shparlinski",
title = "On Curves Over Finite Fields with {Jacobians} of Small
Exponent",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "819--826",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001687",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001687",
abstract = "We show that finite fields over which there is a curve
of a given genus g \geq 1 with its Jacobian having a
small exponent, are very rare. This extends a recent
result of Duke in the case of g = 1. We also show that
when g = 1 or g = 2, our lower bounds on the exponent,
valid for almost all finite fields {$ \mathbb {F}
$}$_q$ and all curves over {$ \mathbb {F} $}$_q$, are
best possible.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Leher:2008:BGN,
author = "Eli Leher",
title = "Bounds for the Genus of Numerical Semigroups",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "827--834",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001699",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001699",
abstract = "We introduce a method to find upper and lower bounds
for the genus of numerical semigroups. Using it we
prove some old and new bounds for it and for the
Frobenius number of the semigroup.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jarden:2008:UFR,
author = "Moshe Jarden and Carlos R. Videla",
title = "Undecidability of Families of Rings of Totally Real
Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "835--850",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001705",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001705",
abstract = "Let {\mathbb{Z}}$_{tr}$ be the ring of totally real
integers, Gal({$ \mathbb {Q}$}) the absolute Galois
group of {$ \mathbb {Q}$}, and e a positive integer.
For each \sigma = (\sigma$_1$, \ldots, \sigma$_e$) \in
Gal({$ \mathbb {Q}$})$^e$ let {\mathbb{Z}}$_{tr}$
(\sigma) be the fixed ring in {\mathbb{Z}}$_{tr}$ of
\sigma$_1$, \ldots, \sigma$_e$. Then, the theory of all
first order sentences \theta that are true in
{\mathbb{Z}}$_{tr}$ (\sigma) for almost all \sigma \in
Gal({$ \mathbb {Q}$})$^e$ (in the sense of the Haar
measure) is undecidable.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zieve:2008:SFP,
author = "Michael E. Zieve",
title = "Some Families of Permutation Polynomials Over Finite
Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "851--857",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001717",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001717",
abstract = "We give necessary and sufficient conditions for a
polynomial of the form x$^r$ (1 + x$^v$ + x$^{2v}$ +
\cdots + x$^{kv}$ )$^t$ to permute the elements of the
finite field {$ \mathbb {F} $}$_q$. Our results yield
especially simple criteria in case (q - 1)/gcd(q - 1,
v) is a small prime.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2008:PIS,
author = "Yuancheng Liu",
title = "On the Problem of Integer Solutions to Decomposable
Form Inequalities",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "5",
pages = "859--872",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001766",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001766",
abstract = "This paper proves a conjecture proposed by Chen and Ru
in [1] on the finiteness of the number of integer
solutions to decomposable form inequalities. Let k be a
number field and let F(X$_1$, \ldots, X$_m$) be a
non-degenerate decomposable form with coefficients in
k. We show that for every finite set of places S of k
containing the archimedean places of k, for each real
number \lambda < 1 and each constant c > 0, the
inequality has only finitely many -non-proportional
solutions, where H$_S$ (x$_1$, \ldots, x$_m$) =
\Pi$_{\upsilon \in S}$ max$_{1 \leq i \leq m}$ ||x$_i$
||$_{\upsilon }$ is the S-height.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rosengren:2008:SSE,
author = "Hjalmar Rosengren",
title = "Sums of Squares from Elliptic {Pfaffians}",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "873--902",
month = dec,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042108001778",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001778",
abstract = "We give a new proof of Milne's formulas for the number
of representations of an integer as a sum of 4m$^2$ and
4m(m + 1) squares. The proof is based on explicit
evaluation of pfaffians with elliptic function entries,
and relates Milne's formulas to Schur Q-polynomials and
to correlation functions for continuous dual Hahn
polynomials. We also state a new formula for 2m$^2$
squares.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Balasuriya:2008:CES,
author = "Sanka Balasuriya and William D. Banks and Igor E.
Shparlinski",
title = "Congruences and Exponential Sums with the Sum of
Aliquot Divisors Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "903--909",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S179304210800178X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210800178X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kamano:2008:ABN,
author = "Ken Kamano",
title = "$p$-adic $q$-{Bernoulli} numbers and their
denominators",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "911--925",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S179304210800181X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210800181X",
abstract = "We define $p$-adic q-Bernoulli numbers by using a
$p$-adic integral. These numbers have good properties
similar to those of the classical Bernoulli numbers. In
particular, they satisfy an analogue of the von
Staudt--Clausen theorem, which includes information of
denominators of $p$-adic q-Bernoulli numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Balandraud:2008:IMN,
author = "{\'E}ric Balandraud",
title = "The Isoperimetric Method in Non-{Abelian} Groups with
an Application to Optimally Small Sumsets",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "927--958",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001821",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001821",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gurak:2008:PHK,
author = "S. Gurak",
title = "Polynomials for Hyper-{Kloosterman} Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "959--972",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001808",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001808",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Luca:2008:DE,
author = "Florian Luca and Alain Togb{\'e}",
title = "On the {Diophantine} equation $ x^2 + 2^a \cdot 5^b =
y^n $",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "973--979",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001791",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001791",
abstract = "In this note, we find all the solutions of the
Diophantine equation x$^2$ + 2$^a$ \cdotp 5$^b$ = y$^n$
in positive integers x, y, a, b, n with x and y coprime
and n \geq 3.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Walling:2008:AHO,
author = "Lynne H. Walling",
title = "Action of {Hecke} Operators on {Siegel} Theta Series,
{II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "981--1008",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001845",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001845",
abstract = "We apply the Hecke operators T(p)$^2$ and (1 \leq j
\leq n \leq 2k) to a degree n theta series attached to
a rank 2k {\mathbb{Z}}-lattice L equipped with a
positive definite quadratic form in the case that L/pL
is regular. We explicitly realize the image of the
theta series under these Hecke operators as a sum of
theta series attached to certain sublattices of,
thereby generalizing the Eichler Commutation Relation.
We then show that the average theta series (averaging
over isometry classes in a given genus) is an eigenform
for these operators. We explicitly compute the
eigenvalues on the average theta series, extending
previous work where we had the restrictions that \chi
(p) = 1 and n \leq k. We also show that for j > k when
\chi (p) = 1, and for j \geq k when \chi (p) = -1, and
that \theta (gen L) is an eigenform for T(p)$^2$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{El-Mahassni:2008:DCD,
author = "Edwin D. El-Mahassni and Domingo Gomez",
title = "On the Distribution of Counter-Dependent Nonlinear
Congruential Pseudorandom Number Generators in Residue
Rings",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "1009--1018",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001857",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001857",
abstract = "Nonlinear congruential pseudorandom number generators
can have unexpectedly short periods. Shamir and Tsaban
introduced the class of counter-dependent generators
which admit much longer periods. In this paper, using a
technique developed by Niederreiter and Shparlinski, we
present discrepancy bounds for sequences of s-tuples of
successive pseudorandom numbers generated by
counter-dependent generators modulo a composite M.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Khanduja:2008:TD,
author = "Sudesh K. Khanduja and Munish Kumar",
title = "On a Theorem of {Dedekind}",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "1019--1025",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001833",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001833",
abstract = "Let K = {$ \mathbb {Q} $}(\theta) be an algebraic
number field with \theta in the ring A$_K$ of algebraic
integers of K and f(x) be the minimal polynomial of
\theta over the field {$ \mathbb {Q}$} of rational
numbers. For a rational prime p, let be the
factorization of the polynomial obtained by replacing
each coefficient of f(x) modulo p into product of
powers of distinct monic irreducible polynomials over
{\mathbb{Z}}/p{\mathbb{Z}}. Dedekind proved that if p
does not divide [A$_K$: {\mathbb{Z}}[\theta ]], then
the factorization of pA$_K$ as a product of powers of
distinct prime ideals is given by, with {$ \mathfrak
{p} $}$_i$ = pA$_K$ + g$_i$ (\theta)A$_K$, and residual
degree. In this paper, we prove that if the
factorization of a rational prime p in A$_K$ satisfies
the above-mentioned three properties, then p does not
divide [A$_K$ :{\mathbb{Z}}[\theta ]]. Indeed the
analogue of the converse is proved for general Dedekind
domains. The method of proof leads to a generalization
of one more result of Dedekind which characterizes all
rational primes p dividing the index of K.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Garthwaite:2008:CMT,
author = "Sharon Anne Garthwaite",
title = "The coefficients of the $ \omega (q) $ mock theta
function",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "1027--1042",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001869",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001869",
abstract = "In 1920, Ramanujan wrote to Hardy about his discovery
of the mock theta functions. In the years since, there
has been much work in understanding the transformation
properties and asymptotic nature of these functions.
Recently, Zwegers proved a relationship between mock
theta functions and vector-valued modular forms, and
Bringmann and Ono used the theory of Maass forms and
Poincar{\'e} series to prove a conjecture of Andrews,
yielding an exact formula for the coefficients of the
f(q) mock theta function. Here we build upon these
results, using the theory of vector-valued modular
forms and Poincar{\'e} series to prove an exact formula
for the coefficients of the \omega (q) mock theta
function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{David:2008:PLA,
author = "Sinnou David and Am{\'i}lcar Pacheco",
title = "Le probl{\`e}me de {Lehmer} ab{\'e}lien pour un module
de {Drinfel'd}. ({French}) [{The} {Lehmer} abelien
problem for a {Drinfel'd} module]",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "1043--1067",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001870",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001870",
abstract = "Let \varphi be a Drinfel'd module defined over a
finite extension K of {$ \mathbb {F} $}$_q$ (T); we
establish a uniform lower bound for the canonical
height of a point of \varphi, rational over the maximal
abelian extension of K, and thus solve the so-called
abelian version of the Lehmer problem in this
situation. The classical original problem (a non
torsion point in {$ \mathbb {G} $}$_m$ ({$ \mathbb
{Q}$}$^{ab}$)) was solved by Amoroso and Dvornicich
[1]. Soit \varphi un module de Drinfel'd d{\'e}fini sur
une extension finie K de {$ \mathbb {F} $}$_q$ (T);
nous d{\'e}montrons une minoration uniforme pour la
hauteur canonique d'un point de \varphi, rationnel sur
l'extension ab{\'e}lienne maximale de K, et
r{\'e}solvons ainsi la version dite ab{\'e}lienne du
probl{\`e}me de Lehmer dans cette situation. Dans le
cadre classique (un point d'ordre infini de {$ \mathbb
{G} $}$_m$ ({$ \mathbb {Q}$}$^{ab}$)), cette question a
{\'e}t{\'e} r{\'e}solue par Amoroso et Dvornicich dans
[1].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Anonymous:2008:AIV,
author = "Anonymous",
title = "Author Index (Volume 4)",
journal = j-INT-J-NUMBER-THEORY,
volume = "4",
number = "6",
pages = "1069--1072",
month = dec,
year = "2008",
DOI = "https://doi.org/10.1142/S1793042108001900",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042108001900",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dewitt:2009:FGR,
author = "Meghan Dewitt and Darrin Doud",
title = "Finding {Galois} Representations Corresponding to
Certain {Hecke} Eigenclasses",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "1--11",
month = feb,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109001888",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001888",
abstract = "In 1992, Ash and McConnell presented computational
evidence of a connection between three-dimensional
Galois representations and certain arithmetic
cohomology classes. For some examples, they were unable
to determine the attached representation. For several
Hecke eigenclasses (including one for which Ash and
McConnell did not find the Galois representation), we
find a Galois representation which appears to be
attached and show strong evidence for the uniqueness of
this representation. The techniques that we use to find
defining polynomials for the Galois representations
include a targeted Hunter search, class field theory
and elliptic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alaca:2009:NRP,
author = "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Mathieu F.
Lemire and Kenneth S. Williams",
title = "The Number of Representations of a Positive Integer by
Certain Quaternary Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "13--40",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001943",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001943",
abstract = "Some theta function identities are proved and used to
give formulae for the number of representations of a
positive integer by certain quaternary forms x$^2$ +
ey$^2$ + fz$^2$ + gt$^2$ with e, f, g \in {1, 2, 4,
8}.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Singh:2009:DPS,
author = "Jitender Singh",
title = "Defining power sums of $n$ and $ \phi (n)$ integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "41--53",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900189X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900189X",
abstract = "Let n be a positive integer and \phi (n) denotes the
Euler phi function. It is well known that the power sum
of n can be evaluated in closed form in terms of n.
Also, the sum of all those \phi (n) positive integers
that are coprime to n and not exceeding n, is
expressible in terms of n and \phi (n). Although such
results already exist in literature, but here we have
presented some new analytical results in these
connections. Some functional and integral relations are
derived for the general power sums.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nathanson:2009:HFP,
author = "Melvyn B. Nathanson",
title = "Heights on the Finite Projective Line",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "55--65",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900192X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900192X",
abstract = "Define the height function h(a) = {mink + (ka mod p) :
k = 1, 2, \ldots, p - 1} for a \in {0, 1, \ldots, p -
1.} It is proved that the height has peaks at p, (p +
1)/2, and (p + c)/3, that these peaks occur at a =
[p/3], (p - 3)/2, (p - 1)/2, [2p/3], p - 3, p 2, and p
- 1, and that h(a) \leq p/3 for all other values of
a.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Azaiez:2009:RHM,
author = "Najib Ouled Azaiez",
title = "Restrictions of {Hilbert} Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "67--80",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001931",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001931",
abstract = "Let \Gamma \subset PSL(2, {\mathbb{R}}) be a discrete
and finite covolume subgroup. We suppose that the
modular curve is ``embedded'' in a Hilbert modular
surface, where \Gamma$_K$ is the Hilbert modular group
associated to a real quadratic field K. We define a
sequence of restrictions (\rho$_n$)$_{n \in \mathbb {N}
}$ of Hilbert modular forms for \Gamma$_K$ to modular
forms for \Gamma. We denote by M$_{k 1}$, k$_2$
(\Gamma$_K$) the space of Hilbert modular forms of
weight (k$_1$, k$_2$) for \Gamma$_K$. We prove that $
\sum_{n \in \mathbb {N} }$ $ \sum_{k 1}$, k$_2$ \in
\mathbb{N} \rho$_n$ (M$_{k 1}$, k$_2$ (\Gamma$_K$)) is
a subalgebra closed under Rankin--Cohen brackets of the
algebra \oplus$_{k \in \mathbb {N} }$ M$_k$ (\Gamma) of
modular forms for \Gamma.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tanner:2009:SCP,
author = "Noam Tanner",
title = "Strings of Consecutive Primes in Function Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "81--88",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001918",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001918",
abstract = "In a recent paper, Thorne [5] proved the existence of
arbitrarily long strings of consecutive primes in
arithmetic progressions in the polynomial ring {$
\mathbb {F} $}$_q$ [t]. Here we extend this result to
show that given any k there exists a string of k
consecutive primes of degree D in arithmetic
progression for {\em all\/} sufficiently large D.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wiese:2009:MSC,
author = "Gabor Wiese",
title = "On Modular Symbols and the Cohomology of {Hecke}
Triangle Surfaces",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "89--108",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001967",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001967",
abstract = "The aim of this article is to give a concise algebraic
treatment of the modular symbols formalism, generalized
from modular curves to Hecke triangle surfaces. A
sketch is included of how the modular symbols formalism
gives rise to the standard algorithms for the
computation of holomorphic modular forms. Precise and
explicit connections are established to the cohomology
of Hecke triangle surfaces and group cohomology. A
general commutative ring is used as coefficient ring in
view of applications to the computation of modular
forms over rings different from the complex numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Weston:2009:PRF,
author = "Tom Weston and Elena Zaurova",
title = "Power Residues of {Fourier} Coefficients of Elliptic
Curves with Complex Multiplication",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "109--124",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001955",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001955",
abstract = "Fix m greater than one and let E be an elliptic curve
over Q with complex multiplication. We formulate
conjectures on the density of primes p (congruent to
one modulo m) for which the pth Fourier coefficient of
E is an mth power modulo p; often these densities
differ from the naive expectation of 1/m. We also prove
our conjectures for m dividing the number of roots of
unity lying in the CM field of E; the most involved
case is m = 4 and complex multiplication by Q(i).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{AlHajjShehadeh:2009:GFH,
author = "Hala {Al Hajj Shehadeh} and Samar Jaafar and Kamal
Khuri-Makdisi",
title = "Generating Functions for {Hecke} Operators",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "125--140",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001979",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001979",
abstract = "Fix a prime N, and consider the action of the Hecke
operator T$_N$ on the space of modular forms of full
level and varying weight \kappa. The coefficients of
the matrix of T$_N$ with respect to the basis {E$_4^i$
E$_6^j$ | 4i + 6j = \kappa } for can be combined for
varying \kappa into a generating function F$_N$. We
show that this generating function is a rational
function for all N, and present a systematic method for
computing F$_N$. We carry out the computations for N =
2, 3, 5, and indicate and discuss generalizations to
spaces of modular forms of arbitrary level.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rhoades:2009:SPD,
author = "Robert C. Rhoades",
title = "Statistics of Prime Divisors in Function Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "141--152",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109001980",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001980",
abstract = "We show that the prime divisors of a random polynomial
in $ \mathbb {F}_q[t] $ are typically ``Poisson
distributed''. This result is analogous to the result
in {\mathbb{Z}} of Granville [1]. Along the way, we use
a sieve developed by Granville and Soundararajan [2] to
give a simple proof of the Erd{\H{o}}s--Kac theorem in
the function field setting. This approach gives
stronger results about the moments of the sequence $
\omega (f)_{f \in { \mathbb {F} } q} [t] $ than was
previously known, where $ \omega (f) $ is the number of
prime divisors of $f$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Raji:2009:FCG,
author = "Wissam Raji",
title = "{Fourier} Coefficients of Generalized Modular Forms of
Negative Weight",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "153--160",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002006",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002006",
abstract = "The Fourier coefficients of classical modular forms of
negative weights have been determined for the case for
which F(\tau) belongs to a subgroup of the full modular
group [9]. In this paper, we determine the Fourier
coefficients of generalized modular forms of negative
weights using the circle method.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Carr:2009:LIR,
author = "Richard Carr and Cormac O'Sullivan",
title = "On the Linear Independence of Roots",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "161--171",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002018",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002018",
abstract = "A set of real nth roots that is pairwise linearly
independent over the rationals must also be linearly
independent. We show how this result may be extended to
more general fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kuo:2009:GST,
author = "Wentang Kuo",
title = "A Generalization of the {Sato--Tate Conjecture}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "1",
pages = "173--184",
month = feb,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900202X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:18 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900202X",
abstract = "The original Sato--Tate Conjecture concerns the angle
distribution of the eigenvalues arisen from non-CM
elliptic curves. In this paper, we formulate an
analogue of the Sato--Tate Conjecture on automorphic
forms of (GL$_n$) and, under a holomorphic assumption,
prove that the distribution is either uniform or the
generalized Sato--Tate measure.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rivoal:2009:AAI,
author = "Tanguy Rivoal",
title = "Applications arithm{\'e}tiques de l'interpolation
lagrangienne. ({French}) [{Arithmetic} applications of
{Lagrangianp} interpolation]",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "185--208",
month = mar,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109001992",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001992",
abstract = "Newton's polynomial interpolation was applied in many
situations in number theory, for example, to prove
Polya's famous theorem on the growth of arithmetic
entire function or the transcendency of e$^{\pi }$ by
Gel'fond. In this paper, we study certain arithmetic
applications of the rational interpolation defined by
Ren{\'e} Lagrange in 1935, which was never done before.
More precisely, we obtain new proofs of the
irrationality of the numbers log(2) and \zeta (3).
Furthermore, we provide a simultaneous generalization
of Newton and Lagrange's interpolations, which enables
us to get the irrationality of \zeta (2).
L'interpolation polynomiale de Newton a eu de tr{\`e}s
nombreuses applications arithm{\'e}tiques en
th{\'e}orie des nombres, comme le c{\'e}l{\`e}bre
th{\'e}or{\`e}me de Polya sur la croissance des
fonctions enti{\`e}res arithm{\'e}tiques ou encore la
transcendance de e$^{\pi }$ par Gel'fond. Dans ce
papier, on pr{\'e}sente certaines applications
arithm{\'e}tiques de l'interpolation rationnelle
d{\'e}finie par Ren{\'e} Lagrange en 1935, ce qui
n'avait jamais {\'e}t{\'e} fait auparavant. On retrouve
ainsi l'irrationalit{\'e} des nombres log(2) et \zeta
(3). On montre ensuite comment g{\'e}n{\'e}raliser
simultan{\'e}ment l'interpolation de Newton et celle de
Lagrange, ce qui nous permet de retrouver
l'irrationalit{\'e} de \zeta (2).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Chaumont:2009:CSL,
author = "Alain Chaumont and Johannes Leicht and Tom M{\"u}ller
and Andreas Reinhart",
title = "The Continuing Search for Large Elite Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "209--218",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002031",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002031",
abstract = "A prime number p is called {\em elite\/} if only
finitely many Fermat numbers 2$^{2 n}$ + 1 are
quadratic residues modulo p. So far, all 21 elite
primes less than 250 billion were known, together with
24 larger items. We completed the systematic search up
to the range of 2.5 \cdotp 10$^{12}$ finding six more
such numbers. Moreover, 42 new elites larger than this
bound were found, among which the largest has 374 596
decimal digits. A survey on the knowledge about elite
primes together with some open problems and conjectures
are presented.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Yee:2009:BPT,
author = "Ae Ja Yee",
title = "Bijective Proofs of a Theorem of {Fine} and Related
Partition Identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "219--228",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002043",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002043",
abstract = "In this paper, we prove a theorem of Fine bijectively.
Stacks with summits and gradual stacks with summits are
also discussed.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bandini:2009:CTE,
author = "A. Bandini and I. Longhi",
title = "Control Theorems for Elliptic Curves Over Function
Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "229--256",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002067",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002067",
abstract = "Let F be a global field of characteristic p > 0, {$
\mathbb {F} $}/F a Galois extension with and E/F a
non-isotrivial elliptic curve. We study the behavior of
Selmer groups Sel$_E$ (L)$_l$ (l any prime) as L varies
through the subextensions of {$ \mathbb {F} $} via
appropriate versions of Mazur's Control Theorem. In the
case l = p, we let {$ \mathbb {F} $} = \cup {$ \mathbb
{F} $}$_d$ where {$ \mathbb {F} $}$_d$ /F is a
-extension. We prove that Sel$_E$ ({$ \mathbb {F}
$}$_d$)$_p$ is a cofinitely generated {\mathbb{Z}}$_p$
[[Gal({\mathbb{Z}}$_d$ /F)]]-module and we associate to
its Pontrjagin dual a Fitting ideal. This allows to
define an algebraic {$L$}-function associated to E in
{\mathbb{Z}}$_p$ [[Gal({\mathbb{Z}}/F)]], providing an
ingredient for a function field analogue of Iwasawa's
Main Conjecture for elliptic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Murty:2009:SVP,
author = "M. Ram Murty and N. Saradha",
title = "Special Values of the Polygamma Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "257--270",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002079",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002079",
abstract = "Let q be a natural number and. We consider the
Dirichlet series $ \sum_{n \geq 1} $ f(n)/n$^s$ and
relate its value when s is a natural number, to the
special values of the polygamma function. For certain
types of functions f, we evaluate the special value
explicitly and use this to study linear independence
over {$ \mathbb {Q}$} of L(k,\chi) as \chi ranges over
Dirichlet characters mod q which have the same parity
as k.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chida:2009:IOS,
author = "Masataka Chida",
title = "Indivisibility of Orders of {Selmer} Groups for
Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "271--280",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002080",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002080",
abstract = "In this paper, we consider indivisibility of orders of
Selmer groups for modular forms under quadratic twists.
Then, we will give a generalization of a theorem of
James--Ono and Kohnen--Ono.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kumchev:2009:BAE,
author = "Angel V. Kumchev",
title = "A Binary Additive Equation Involving Fractional
Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "281--292",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002092",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002092",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Li:2009:EPD,
author = "Xian-Jin Li",
title = "On the {Euler} Product of the {Dedekind} Zeta
Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "293--301",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002109",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002109",
abstract = "It is well known that the Euler product formula for
the Riemann zeta function \zeta (s) is still valid for
{\mathfrak{R}}(s) = 1 and s \neq 1. In this paper, we
extend this result to zeta functions of number fields.
In particular, we show that the Dedekind zeta function
\zeta$_k$ (s) for any algebraic number field k can be
written as the Euler product on the line
{\mathfrak{R}}(s) = 1 except at the point s = 1. As a
corollary, we obtain the Euler product formula on the
line {\mathfrak{R}}(s) = 1 for Dirichlet
{$L$}-functions L(s, \chi) of real characters.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Folsom:2009:CMU,
author = "Amanda Folsom",
title = "A Characterization of the Modular Units",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "303--310",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002110",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002110",
abstract = "We provide an exact formula for the complex exponents
in the modular product expansion of the modular units
in terms of the Kubert--Lang structure theory, and
deduce a characterization of the modular units in terms
of the growth of these exponents, answering a question
posed by Kohnen.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nitaj:2009:CRCo,
author = "Abderrahmane Nitaj",
title = "Cryptanalysis of {RSA} with Constrained Keys",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "311--325",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002122",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002122",
abstract = "Let n = pq be an RSA modulus with unknown prime
factors of equal bit-size. Let e be the public exponent
and d be the secret exponent satisfying ed \equiv 1 mod
\varphi (n) where \varphi (n) is the Euler totient
function. To reduce the decryption time or the
signature generation time, one might be tempted to use
a small private exponent d. Unfortunately, in 1990,
Wiener showed that private exponents smaller than are
insecure and in 1999, Boneh and Durfee improved the
bound to n$^{0.292}$. In this paper, we show that
instances of RSA with even large private exponents can
be efficiently broken if there exist positive integers
X, Y such that |eY - XF(u)| and Y are suitably small
where F is a function of publicly known expression for
which there exists an integer u \neq 0 satisfying F(u)
\approx n and pu or qu is computable from F(u) and n.
We show that the number of such exponents is at least
O(n$^{3 / 4 - \varepsilon }$) when F(u) = p(q - u).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Andrews:2009:SIA,
author = "George E. Andrews and Sylvie Corteel and Carla D.
Savage",
title = "On $q$-series identities arising from lecture hall
partitions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "327--337",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002134",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002134",
abstract = "In this paper, we highlight two $q$-series identities
arising from the ``five guidelines'' approach to
enumerating lecture hall partitions and give direct,
$q$-series proofs. This requires two new finite
corollaries of a q-analog of Gauss's second theorem. In
fact, the method reveals stronger results about lecture
hall partitions and anti-lecture hall compositions that
are only partially explained combinatorially.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pila:2009:EFS,
author = "Jonathan Pila",
title = "Entire Functions Sharing Arguments of Integrality,
{I}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "339--353",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002146",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002146",
abstract = "Let f be an entire function that is real and strictly
increasing for all sufficiently large real arguments,
and that satisfies certain additional conditions, and
let X$_f$ be the set of non-negative real numbers at
which f is integer valued. Suppose g is an entire
function that takes integer values on X$_f$. We find
growth conditions under which f,g must be algebraically
dependent (over {\mathbb{Z}}) on X. The result
generalizes a weak form of a theorem of P{\'o}lya.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tanigawa:2009:FPM,
author = "Yoshio Tanigawa and Wenguang Zhai",
title = "On the fourth power moment of {$ \Delta x $} and {$
E(x) $} in short intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "2",
pages = "355--382",
month = mar,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002055",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002055",
abstract = "Let \Delta (x) and E(x) be error terms of the sum of
divisor function and the mean square of the Riemann
zeta function, respectively. In this paper, their
fourth power moments for short intervals of Jutila's
type are considered. We get an asymptotic formula for U
in some range.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sands:2009:VFM,
author = "Jonathan W. Sands",
title = "Values at $ s = - 1 $ of {$L$}-functions for
multi-quadratic extensions of number fields, and the
fitting ideal of the tame kernel",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "383--405",
month = may,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109002183",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002183",
abstract = "Fix a Galois extension of totally real number fields
such that the Galois group G has exponent 2. Let S be a
finite set of primes of F containing the infinite
primes and all those which ramify in, let denote the
primes of lying above those in S, and let denote the
ring of -integers of. We then compare the Fitting ideal
of as a {\mathbb{Z}}[G]-module with a higher
Stickelberger ideal. The two extend to the same ideal
in the maximal order of {$ \mathbb {Q} $}[G], and hence
in {\mathbb{Z}}[1/2][G]. Results in {\mathbb{Z}}[G] are
obtained under the assumption of the Birch--Tate
conjecture, especially for biquadratic extensions,
where we compute the index of the higher Stickelberger
ideal. We find a sufficient condition for the Fitting
ideal to contain the higher Stickelberger ideal in the
case where is a biquadratic extension of F containing
the first layer of the cyclotomic
{\mathbb{Z}}$_2$-extension of F, and describe a class
of biquadratic extensions of F = {$ \mathbb {Q}$} that
satisfy this condition.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baccar:2009:SSP,
author = "N. Baccar and F. {Ben Sa{\"i}d}",
title = "On Sets Such That the Partition Function Is Even from
a Certain Point On",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "407--428",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002195",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002195",
abstract = "Let P \in {$ \mathbb {F} $}$_2$ [z] with P(0) = 1 and
degree(P) \geq 1. It is not difficult to prove (cf.
[4,14]) that there is a unique subset of \mathbb{N}
such that (mod 2), where denotes the number of
partitions of n with parts in. However, finding the
elements of such sets for general P seems to be hard.
In this paper, we obtain solutions to this problem for
a large class of polynomials P. Moreover, we give
asymptotics for the counting function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chu:2009:ISH,
author = "Wenchang Chu and Deyin Zheng",
title = "Infinite Series with Harmonic Numbers and Central
Binomial Coefficients",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "429--448",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002171",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002171",
abstract = "By means of two hypergeometric summation formulae, we
establish two large classes of infinite series
identities with harmonic numbers and central binomial
coefficients. Up to now, these numerous formulae have
hidden behind very few known identities of
Ap{\'e}ry-like series for Riemann-zeta function,
discovered mainly by Lehmer [14] and Elsner [12] as
well as Borwein {\em et al.\/} [4, 5, 7]. All the
computation and verification are carried out by an
appropriately-devised {\em Mathematica\/} package.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ding:2009:SIF,
author = "Shanshan Ding",
title = "Smallest irreducible of the form $ x^2 - d y^2 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "449--456",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002158",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002158",
abstract = "It is a classical result that prime numbers of the
form x$^2$ + ny$^2$ can be characterized via class
field theory for an infinite set of n. In this paper,
we derive the function field analogue of the classical
result. Then, we apply an effective version of the
Chebotarev density theorem to bound the degree of the
smallest irreducible of the form x$^2$- dy$^2$, where
x, y, and d are elements of a polynomial ring over a
finite field.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kominers:2009:CEE,
author = "Scott Duke Kominers",
title = "Configurations of Extremal Even Unimodular Lattices",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "457--464",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900216X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900216X",
abstract = "We extend the results of Ozeki on the configurations
of extremal even unimodular lattices. Specifically, we
show that if L is such a lattice of rank 56, 72, or 96,
then L is generated by its minimal-norm vectors.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Akbary:2009:RSM,
author = "Amir Akbary and V. Kumar Murty",
title = "Reduction $ \bmod p $ of subgroups of the
{Mordell--Weil} group of an elliptic curve",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "465--487",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002225",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002225",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kurlberg:2009:PSS,
author = "P{\"a}r Kurlberg",
title = "{Poisson} Spacing Statistics for Value Sets of
Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "489--513",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002237",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002237",
abstract = "If f is a non-constant polynomial with integer
coefficients and q is an integer, we may regard f as a
map from Z/qZ to Z/qZ. We show that the distribution of
the (normalized) spacings between consecutive elements
in the image of these maps becomes {\em Poissonian\/}
as q tends to infinity along any sequence of square
free integers such that the mean spacing modulo q tends
to infinity.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Shavgulidze:2009:NRI,
author = "Ketevan Shavgulidze",
title = "On the Number of Representations of Integers by the
Sums of Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "515--525",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002201",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002201",
abstract = "We shall obtain the formulae for the number of
representations of positive integers by a direct sum of
k binary quadratic forms of the kind, when k = 3, 4,
5.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bosca:2009:PIA,
author = "S{\'e}bastien Bosca",
title = "Principalization of Ideals in {Abelian} Extensions of
Number Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "527--539",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002213",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002213",
abstract = "We give a self-contained proof of a general conjecture
of Gras on principalization of ideals in Abelian
extensions of a given field L, which was solved by
Kurihara in the case of totally real extensions L of
the rational field {$ \mathbb {Q} $}. More precisely,
for any given extension L/K of number fields, in which
at least one infinite place of K totally splits, and
for any ideal class c$_L$ of L, we construct a finite
Abelian extension F/K, in which all infinite places
totally split, such that c$_L$ become principal in the
compositum M = LF.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sapar:2009:MEA,
author = "S. H. Sapar and K. A. Mohd. Atan",
title = "A method of estimating the $p$-adic sizes of common
zeros of partial derivative polynomials associated with
a quintic form",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "3",
pages = "541--554",
month = may,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002249",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:19 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002249",
abstract = "It is known that the value of the exponential sum can
be derived from the estimate of the cardinality |V|,
the number of elements contained in the set where is
the partial derivatives of with respect to. The
cardinality of V in turn can be derived from the
$p$-adic sizes of common zeros of the partial
derivatives. This paper presents a method of
determining the $p$-adic sizes of the components of
(\xi, \eta) a common root of partial derivative
polynomials of f(x,y) in $ Z_p$ [x,y] of degree five
based on the $p$-adic Newton polyhedron technique
associated with the polynomial. The degree five
polynomial is of the form f(x,y) = ax$^5$ + bx$^4$ y +
cx$^3$ y$^2$ + sx + ty + k. The estimate obtained is in
terms of the $p$-adic sizes of the coefficients of the
dominant terms in f.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kida:2009:QPH,
author = "Masanari Kida and Gu{\'e}na{\"e}l Renault and Kazuhiro
Yokoyama",
title = "Quintic Polynomials of {Hashimoto--Tsunogai}, {Brumer}
and {Kummer}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "555--571",
month = jun,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109002250",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002250",
abstract = "We establish an isomorphism between the quintic cyclic
polynomials discovered by Hashimoto--Tsunogai and those
arising from Kummer theory for certain algebraic tori.
This enables us to solve the isomorphism problem for
Hashimoto--Tsunogai polynomials and also Brumer's
quintic polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bringmann:2009:CDR,
author = "Kathrin Bringmann",
title = "Congruences for {Dyson}'s Ranks",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "573--584",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002262",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002262",
abstract = "In this paper, we prove infinite families of
congruences for coefficients of harmonic Maass forms
whose coefficients encode Dyson's rank. This
generalizes the earlier joint work of the author with
Ken Ono.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alvanos:2009:CAC,
author = "Paraskevas Alvanos and Yuri Bilu and Dimitrios
Poulakis",
title = "Characterizing Algebraic Curves with Infinitely Many
Integral Points",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "585--590",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002274",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002274",
abstract = "A classical theorem of Siegel asserts that the set of
S-integral points of an algebraic curveC over a number
field is finite unless C has genus 0 and at most two
points at infinity. In this paper, we give necessary
and sufficient conditions for C to have infinitely many
S-integral points.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kozuma:2009:ECR,
author = "Rintaro Kozuma",
title = "Elliptic Curves Related to Cyclic Cubic Extensions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "591--623",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002304",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002304",
abstract = "The aim of this paper is to study certain family of
elliptic curves defined over a number field F arising
from hyperplane sections of some cubic surface
associated to a cyclic cubic extension K/F. We show
that each admits a 3-isogeny \varphi over F and the
dual Selmer group is bounded by a kind of unit/class
groups attached to K/F. This is proven via certain
rational function on the elliptic curve with nice
property. We also prove that the Shafarevich--Tate
group coincides with a class group of K as a special
case.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Konyagin:2009:SPC,
author = "Sergei V. Konyagin and Melvyn B. Nathanson",
title = "Sums of Products of Congruence Classes and of
Arithmetic Progressions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "625--634",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002286",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002286",
abstract = "Consider the congruence class R$_m$ (a) = {a + im : i
\in Z} and the infinite arithmetic progression P$_m$
(a) = {a + im : i \in N$_0$ }. For positive integers
a,b,c,d,m the sum of products set R$_m$ (a)R$_m$ (b) +
R$_m$ (c)R$_m$ (d) consists of all integers of the form
(a+im) \cdotp (b+jm)+(c+km)(d+\ell m) for some
i,j,k,\ell \in Z. It is proved that if gcd(a,b,c,d,m) =
1, then R$_m$ (a)R$_m$ (b) + R$_m$ (c)R$_m$ (d) is
equal to the congruence class R$_m$ (ab+cd), and that
the sum of products set P$_m$ (a)P$_m$ (b)+P$_m$
(c)P$_m$ eventually coincides with the infinite
arithmetic progression P$_m$ (ab+cd).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Oura:2009:EPA,
author = "Manabu Oura",
title = "{Eisenstein} Polynomials Associated to Binary Codes",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "635--640",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002298",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002298",
abstract = "The Eisenstein polynomial is the weighted sum of the
weight enumerators of all classes of Type II codes of
fixed length. In this note, we investigate the ring
generated by Eisenstein polynomials in genus 2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Moree:2009:PPA,
author = "P. Moree and B. Sury",
title = "Primes in a Prescribed Arithmetic Progression Dividing
the Sequence",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "641--665",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002316",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002316",
abstract = "Given positive integers a,b,c and d such that c and d
are coprime, we show that the primes p \equiv c (mod d)
dividing a$^k$ +b$^k$ for some k \geq 1 have a natural
density and explicitly compute this density. We
demonstrate our results by considering some claims of
Fermat that he made in a 1641 letter to Mersenne.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tretkoff:2009:TSV,
author = "Marvin D. Tretkoff and Paula Tretkoff",
title = "Transcendence of Special Values of {Pochhammer}
Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "667--677",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900233X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900233X",
abstract = "In this paper, we examine the set of algebraic numbers
at which higher order hypergeometric functions take
algebraic values. In particular, we deduce criteria for
this set to be finite and for it to be infinite.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vulakh:2009:MSC,
author = "L. Ya. Vulakh",
title = "The {Markov} Spectra for Cocompact {Fuchsian} Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "679--718",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002341",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002341",
abstract = "Applying the Klein model D$^2$ of the hyperbolic plane
and identifying the geodesics in D$^2$ with their poles
in the projective plane, the author has developed a
method for finding the discrete part of the Markov
spectrum for Fuchsian groups. It is applicable mostly
to non-cocompact groups. In the present paper, this
method is extended to cocompact Fuchsian groups. For a
group with signature (0;2,2,2,3), the complete
description of the discrete part of the Markov spectrum
is obtained. The result obtained leads to the complete
description of the Markov and Lagrange spectra for the
imaginary quadratic field with discriminant -20.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hofer:2009:DPG,
author = "Roswitha Hofer and Peter Kritzer and Gerhard Larcher
and Friedrich Pillichshammer",
title = "Distribution properties of generalized {Van Der
Corput--Halton} sequences and their subsequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "4",
pages = "719--746",
month = jun,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002328",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002328",
abstract = "We study the distribution properties of sequences
which are a generalization of the well-known van der
Corput--Halton sequences on one hand, and digital
(T,s)-sequences on the other. In this paper, we give
precise results concerning the distribution properties
of such sequences in the s-dimensional unit cube.
Moreover, we consider subsequences of the
above-mentioned sequences and study their distribution
properties. Additionally, we give discrepancy estimates
for some special cases, including subsequences of van
der Corput and van der Corput--Halton sequences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Adolphson:2009:ESI,
author = "Alan Adolphson and Steven Sperber",
title = "Exponential sums on {$ \mathbb {A}^n $}. {IV}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "747--764",
month = aug,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109002353",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002353",
abstract = "We find new conditions on a polynomial over a finite
field that guarantee that the exponential sum defined
by the polynomial has only one nonvanishing $p$-adic
cohomology group, hence the {$L$}-function associated
to the exponential sum is a polynomial or the
reciprocal of a polynomial.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cooper:2009:CES,
author = "Shaun Cooper",
title = "Construction of {Eisenstein} series for {$ \Gamma_0
(p) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "765--778",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002365",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002365",
abstract = "A simple construction of Eisenstein series for the
congruence subgroup \Gamma$_0$ (p) is given. The
construction makes use of the Jacobi triple product
identity and Gauss sums, but does not use the modular
transformation for the Dedekind eta-function. All
positive integral weights are handled in the same way,
and the conditionally convergent cases of weights 1 and
2 present no extra difficulty.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Salle:2009:MPG,
author = "Landry Salle",
title = "Mild pro-$p$-groups as {Galois} groups over global
fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "779--795",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002377",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002377",
abstract = "This paper is devoted to finding new examples of mild
pro-p-groups as Galois groups over global fields,
following the work of Labute ([6]). We focus on the
Galois group of the maximal T-split S-ramified
pro-p-extension of a global field k. We first retrieve
some facts on presentations of such a group, including
a study of the local-global principle for the
cohomology group, then we show separately in the case
of function fields and in the case of number fields how
it can be used to find some mild pro-p-groups.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Byard:2009:TPQ,
author = "Kevin Byard",
title = "Tenth Power Qualified Residue Difference Sets",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "797--803",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002389",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002389",
abstract = "Qualified residue difference sets of power n are known
to exist for n = 2, 4, 6, as do similar sets that
include the zero element, while both classes of set are
known to be nonexistent for n = 8. Both classes of set
are proved nonexistent for n = 10.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Taylor:2009:ACN,
author = "Karen Taylor",
title = "Analytic Continuation of Nonanalytic Vector-Valued
{Eisenstein} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "805--830",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002407",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002407",
abstract = "In this paper, we introduce a vector-valued
nonanalytic Eisenstein series appearing naturally in
the Rankin--Selberg convolution of a vector-valued
modular cusp form associated to a monomial
representation \rho of SL(2,{\mathbb{Z}}). This
vector-valued Eisenstein series transforms under a
representation \chi$_{\rho }$ associated to \rho. We
use a method of Selberg to obtain an analytic
continuation of this vector-valued nonanalytic
Eisenstein series to the whole complex plane.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jaafar:2009:M,
author = "Samar Jaafar and Kamal Khuri-Makdisi",
title = "On the maps from {$ X(4 p) $} to {$ X(4) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "831--844",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002390",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002390",
abstract = "We study pullbacks of modular forms of weight 1 from
the modular curve X(4) to the modular curve X(4p),
where p is an odd prime. We find the extent to which
such modular forms separate points on X(4p). Our main
result is that these modular forms give rise to a
morphism F from the quotient of X(4p) by a certain
involution \iota to projective space, such that F is a
projective embedding of X(4p)/\iota away from the
cusps. We also report on computer calculations
regarding products of such modular forms, going up to
weight 4 for p \leq 13, and up to weight 3 for p \leq
23, and make a conjecture about these products and the
nature of the singularities at the cusps of the image
F(X(4p)/\iota).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knopp:2009:PGM,
author = "Marvin Knopp and Geoffrey Mason",
title = "Parabolic Generalized Modular Forms and Their
Characters",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "845--857",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002419",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See revisions \cite{Knopp:2012:RPG}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002419",
abstract = "We make a detailed study of the {\em generalized
modular forms\/} of weight zero and their associated
multiplier systems (characters) on an arbitrary
subgroup \Gamma of finite index in the modular group.
Among other things, we show that every generalized
divisor on the compact Riemann surface associated to
\Gamma is the divisor of a modular form (with {\em
unitary\/} character) which is unique up to scalars.
This extends a result of Petersson, and has
applications to the Eichler cohomology.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Suarez:2009:MLC,
author = "Ivan Suarez",
title = "Modular Lattices Over {CM} Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "859--869",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002420",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002420",
abstract = "We study some properties of Arakelov-modular lattices,
which are particular modular ideal lattices over CM
fields. There are two main results in this paper. The
first one is the determination of the number of
Arakelov-modular lattices of fixed level over a given
CM field provided that an Arakelov-modular lattice is
already known. This number depends on the class numbers
of the CM field and its maximal totally real subfield.
The first part gives also a way to compute all these
Arakelov-modular lattices. In the second part, we
describe the levels that can occur for some
multiquadratic CM number fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
keywords = "CM (complex multiplication)",
}
@Article{Angles:2009:WNC,
author = "Bruno Angl{\`e}s and Tatiana Beliaeva",
title = "On {Weil} Numbers in Cyclotomic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "871--884",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002432",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002432",
abstract = "In this paper, we study the $p$-adic behavior of Weil
numbers in the cyclotomic {\mathbb{Z}}$_p$-extension of
the pth cyclotomic field. We determine the
characteristic ideal of the quotient of semi-local
units by Weil numbers in terms of the characteristic
ideals of some classical modules that appear in the
Iwasawa theory. In a recent preprint [9] by Nguyen
Quang Do and Nicolas, a generalization of this result
to a semi-simple case was obtained.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dobi:2009:SRT,
author = "Doris Dobi and Nicholas Wage and Irena Wang",
title = "Supersingular Rank Two {Drinfel'd} Modules and Analogs
of {Atkin}'s Orthogonal Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "885--895",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002444",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002444",
abstract = "The theory of elliptic curves and modular forms
provides a precise relationship between the
supersingular j-invariants and the congruences between
modular forms. Kaneko and Zagier discuss a surprising
generalization of these results in their paper on Atkin
orthogonal polynomials. In this paper, we define an
analog of the Atkin orthogonal polynomials for rank two
Drinfel'd modules.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Glass:2009:RHC,
author = "Darren Glass",
title = "The $2$-Ranks of Hyperelliptic Curves with Extra
Automorphisms",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "897--910",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002468",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002468",
abstract = "This paper examines the relationship between the
automorphism group of a hyperelliptic curve defined
over an algebraically closed field of characteristic
two and the 2-rank of the curve. In particular, we
exploit the wild ramification to use the
Deuring--Shafarevich formula in order to analyze the
ramification of hyperelliptic curves that admit extra
automorphisms and use this data to impose restrictions
on the genera and 2-ranks of such curves. We also show
how some of the techniques and results carry over to
the case where our base field is of characteristic p >
2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Delaunay:2009:SPE,
author = "Christophe Delaunay and Christian Wuthrich",
title = "Self-Points on Elliptic Curves of Prime Conductor",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "5",
pages = "911--932",
month = aug,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002456",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002456",
abstract = "Let E be an elliptic curve of conductor p. Given a
cyclic subgroup C of order p in E[p], we construct a
modular point P$_C$ on E, called self-point, as the
image of (E,C) on X$_0$ (p) under the modular
parametrization X$_0$ (p) \rightarrow E. We prove that
the point is of infinite order in the Mordell--Weil
group of E over the field of definition of C. One can
deduce a lower bound on the growth of the rank of the
Mordell--Weil group in its PGL$_2$
({\mathbb{Z}}$_p$)-tower inside {$ \mathbb
{Q}$}(E[p$^{\infty }$ ]).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Languasco:2009:CRE,
author = "Alessandro Languasco",
title = "A Conditional Result on the Exceptional Set for
{Hardy--Littlewood} Numbers in Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "933--951",
month = sep,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S179304210900247X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900247X",
abstract = "Assuming the Generalized Riemann Hypothesis holds, we
prove some conditional estimates on the exceptional set
in short intervals for the Hardy--Littlewood problem.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bajnok:2009:MSS,
author = "B{\'e}la Bajnok",
title = "On the maximum size of a $ (k, l)$-sum-free subset of
an abelian group",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "953--971",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002481",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002481",
abstract = "A subset A of a given finite abelian group G is called
(k,l)-sum-free if the sum of k (not necessarily
distinct) elements of A does not equal the sum of l
(not necessarily distinct) elements of A. We are
interested in finding the maximum size \lambda$_{k, l}$
(G) of a (k,l)-sum-free subset in G. A (2,1)-sum-free
set is simply called a sum-free set. The maximum size
of a sum-free set in the cyclic group {\mathbb{Z}}$_n$
was found almost 40 years ago by Diamanda and Yap; the
general case for arbitrary finite abelian groups was
recently settled by Green and Ruzsa. Here we find the
value of \lambda$_{3, 1}$ ({\mathbb{Z}}$_n$). More
generally, a recent paper by Hamidoune and Plagne
examines (k,l)-sum-free sets in G when $k - l$ and the
order of G are relatively prime; we extend their
results to see what happens without this assumption.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Luca:2009:MFP,
author = "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}",
title = "On {Machin}'s Formula with Powers of the {Golden}
Section",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "973--979",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002493",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002493",
abstract = "In this note, we find all solutions of the equation
\pi /4 = a arctan(\varphi$^{\kappa }$) + b
arctan(\varphi$^{\ell }$), in integers \kappa and \ell
and rational numbers a and b, where \varphi is the
golden section.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hegyvari:2009:ICL,
author = "Norbert Hegyv{\'a}ri and Fran{\c{c}}ois Hennecart and
Alain Plagne",
title = "Iterated Compositions of Linear Operations on Sets of
Positive Upper Density",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "981--997",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900250X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900250X",
abstract = "Starting from a result of Stewart, Tijdeman and Ruzsa
on iterated difference sequences, we introduce the
notion of iterated compositions of linear operations.
We prove a general result on the stability of such
compositions (with bounded coefficients) on sets of
integers having a positive upper density.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jones:2009:PVT,
author = "Lenny Jones",
title = "Polynomial Variations on a Theme of {Sierpi{\'n}ski}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "999--1015",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002511",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002511",
abstract = "In 1960, Sierpi{\'n}ski proved that there exist
infinitely many odd positive integers k such that k
\cdotp 2$^n$ + 1 is composite for all integers n \geq
0. Variations of this problem, using polynomials with
integer coefficients, and considering reducibility over
the rationals, have been investigated by several
authors. In particular, if S is the set of all positive
integers d for which there exists a polynomial f(x) \in
{\mathbb{Z}}[x], with f(1) \neq -d, such that f(x)x$^n$
+ d is reducible over the rationals for all integers n
\geq 0, then what are the elements of S? Interest in
this problem stems partially from the fact that if S
contains an odd integer, then a question of Erd{\H{o}}s
and Selfridge concerning the existence of an odd
covering of the integers would be resolved. Filaseta
has shown that S contains all positive integers d
\equiv 0 (mod 4), and until now, nothing else was known
about the elements of S. In this paper, we show that S
contains infinitely many positive integers d \equiv 6
(mod 12). We also consider the corresponding problem
over {$ \mathbb {F} $}$_p$, and in that situation, we
show 1 \in S for all primes p.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baier:2009:PQP,
author = "Stephan Baier and Liangyi Zhao",
title = "On Primes in Quadratic Progressions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1017--1035",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002523",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002523",
abstract = "We verify the Hardy--Littlewood conjecture on primes
in quadratic progressions on average. The results in
the present paper significantly improve those of a
previous paper by the authors [3].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dubickas:2009:FPR,
author = "Art{\=u}ras Dubickas",
title = "On the Fractional Parts of Rational Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1037--1048",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002535",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002535",
abstract = "Let \xi be a non-zero real number, and let a = p/q > 1
be a rational number. We denote by U(a,\xi) and
L(a,\xi) the largest and the smallest limit points of
the sequence of fractional parts {\xi a$^n$ }, n =
0,1,2,\ldots, respectively. A possible way to prove
Mahler's conjecture claiming that Z-numbers do not
exist is to show that U(3/2,\xi) > 1/2 for every \xi >
0. We prove that U(3/2,\xi) cannot belong to [0,1/3)
\cup S, where S is an explicit infinite union of
intervals in (1/3,1/2). This result is a corollary to a
more general result claiming that, for any rational a >
1, U(a,\xi) cannot lie in a certain union of intervals.
We also obtain new inequalities for the difference
U(a,\xi) - L(a,\xi). Using them we show that some
analogues of Z-numbers do not exist.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knopp:2009:ECG,
author = "Marvin Knopp and Joseph Lehner and Wissam Raji",
title = "{Eichler} Cohomology for Generalized Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1049--1059",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002547",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002547",
abstract = "By using Stokes's theorem, we prove an Eichler
cohomology theorem for generalized modular forms with
some restrictions on the relevant multiplier systems.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Katsurada:2009:DAA,
author = "Masanori Katsurada and Takumi Noda",
title = "Differential Actions on the Asymptotic Expansions of
Non-Holomorphic {Eisenstein} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1061--1088",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002559",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002559",
abstract = "Let k be an arbitrary even integer, and E$_k$ (s;z)
denote the non-holomorphic Eisenstein series (of weight
k attached to SL$_2$ ({\mathbb{Z}})), defined by (1.1)
below. In the present paper we first establish a
complete asymptotic expansion of E$_k$ (s;z) in the
descending order of y as y \rightarrow + \infty
(Theorem 2.1), upon transferring from the previously
derived asymptotic expansion of E$_0$ (s;z) (due to the
first author [16]) to that of E$_k$ (s;z) through
successive use of Maass' weight change operators.
Theorem 2.1 yields various results on E$_k$ (s;z),
including its functional properties (Corollaries
2.1--2.3), its relevant specific values (Corollaries
2.4--2.7), and its asymptotic aspects as z \rightarrow
0 (Corollary 2.8). We then apply the non-Euclidean
Laplacian \Delta$_{H, k}$ (of weight k attached to the
upper-half plane) to the resulting expansion, in order
to justify the eigenfunction equation for E$_k$ (s;z)
in (1.6), where the justification can be made uniformly
in the whole s-plane (Theorem 2.2).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pong:2009:LSN,
author = "Wai Yan Pong",
title = "Length Spectra of Natural Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1089--1102",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002584",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002584",
abstract = "A natural number n can generally be written as a sum
of m consecutive natural numbers for various values of
m \geq 1. The length spectrum of n is the set of these
admissible m. Two numbers are spectral equivalent if
they have the same length spectrum. We show how to
compute the equivalence classes of this relation.
Moreover, we show that these classes can only have
either 1,2 or infinitely many elements.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pries:2009:TCL,
author = "Rachel Pries",
title = "The $p$-torsion of curves with large $p$-rank",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1103--1116",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002560",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002560",
abstract = "Consider the moduli space of smooth curves of genus g
and $p$-rank f defined over an algebraically closed
field k of characteristic p. It is an open problem to
classify which group schemes occur as the $p$-torsion
of the Jacobians of these curves for f < g - 1. We
prove that the generic point of every component of this
moduli space has a-number 1 when f = g - 2 and f = g -
3. Likewise, we show that a generic hyperelliptic curve
with $p$-rank g 2 has a-number 1 when p \geq 3. We also
show that the locus of curves with $p$-rank g - 2 and
a-number 2 is non-empty with codimension 3 in when p
\geq 5. We include some other results when f = g - 3.
The proofs are by induction on g while fixing g - f.
They use computations about certain components of the
boundary of.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Muriefah:2009:DE,
author = "Fadwa S. Abu Muriefah and Florian Luca and Samir
Siksek and Szabolcs Tengely",
title = "On the {Diophantine} equation {$ x^2 + C = 2 y^n $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1117--1128",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002572",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002572",
abstract = "In this paper, we study the Diophantine equation x$^2$
+ C = 2y$^n$ in positive integers x,y with gcd(x,y) =
1, where n \geq 3 and C is a positive integer. If C
\equiv 1 (mod 4), we give a very sharp bound for prime
values of the exponent n; our main tool here is the
result on existence of primitive divisors in Lehmer
sequences due to Bilu, Hanrot and Voutier. We
illustrate our approach by solving completely the
equations x$^2$ + 17$^{a 1}$ = 2y$^n$, x$^2$ + 5$^{a
1}$ 13$^{a 2}$ = 2y$^n$ and x$^2$ + 3$^{a 1}$ 11$^{a
2}$ = 2y$^n$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chen:2009:GSP,
author = "Sin-Da Chen and Sen-Shan Huang",
title = "On General Series--Product Identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "6",
pages = "1129--1148",
month = sep,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002596",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:20 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002596",
abstract = "We derive the general series--product identities from
which we deduce several applications, including an
identity of Gauss, the generalization of Winquist's
identity by Carlitz and Subbarao, an identity for, the
quintuple product identity, and the octuple product
identity.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2009:GRT,
author = "Yu-Ru Liu and Craig V. Spencer",
title = "A Generalization of {Roth}'s Theorem in Function
Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1149--1154",
month = nov,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109002602",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002602",
abstract = "Let {$ \mathbb {F} $}$_q$ [t] denote the polynomial
ring over the finite field {$ \mathbb {F} $}$_q$, and
let denote the subset of {$ \mathbb {F} $}$_q$ [t]
containing all polynomials of degree strictly less than
N. For non-zero elements r$_1$, \ldots, r$_s$ of {$
\mathbb {F} $}$_q$ satisfying r$_1$ + \cdots + r$_s$ =
0, let denote the maximal cardinality of a set which
contains no non-trivial solution of r$_1$ x$_1$ +
\cdots + r$_s$ x$_s$ = 0 with x$_i$ \in A (1 \leq i
\leq s). We prove that.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bayer-Fluckiger:2009:EMC,
author = "Eva Bayer-Fluckiger and Jean-Paul Cerri and
J{\'e}r{\^o}me Chaubert",
title = "{Euclidean} Minima and Central Division Algebras",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1155--1168",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002614",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002614",
abstract = "The notion of Euclidean minimum of a number field is a
classical one. In this paper, we generalize it to
central division algebras and establish some general
results in this new context.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2009:NLT,
author = "Huaning Liu",
title = "A note on {Lehmer} $k$-tuples",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1169--1178",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002626",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002626",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kuo:2009:GLD,
author = "Wentang Kuo and Yu-Ru Liu",
title = "{Gaussian} Laws on {Drinfeld} Modules",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1179--1203",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002638",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002638",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Belliard:2009:ACC,
author = "Jean-Robert Belliard",
title = "Asymptotic Cohomology of Circular Units",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1205--1219",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S179304210900264X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304210900264X",
abstract = "Let F be a number field, abelian over {$ \mathbb {Q}
$}, and fix a prime p \neq 2. Consider the cyclotomic
{\mathbb{Z}}$_p$-extension F$_{\infty }$ /F and denote
F$_n$ the nth finite subfield and C$_n$ its group of
circular units as defined by Sinnott. Then the Galois
groups G$_{m, n}$ = Gal(F$_m$ /F$_n$) act naturally on
the C$_m$ 's (for any m \geq n \gg 0). We compute the
Tate cohomology groups for i = -1,0 without assuming
anything else neither on F nor on p.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Olofsson:2009:LRH,
author = "Rikard Olofsson",
title = "Local {Riemann} Hypothesis for Complex Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1221--1230",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002651",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002651",
abstract = "In this paper, a special class of local \zeta
functions is studied. The main theorem states that the
functions have all zeros on the line {\mathfrak{R}}(s)
= 1/2. This is a natural generalization of the result
of Bump and Ng stating that the zeros of the Mellin
transform of Hermite functions have {\mathfrak{R}}(s) =
1/2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bundschuh:2009:ARC,
author = "Peter Bundschuh and Keijo V{\"a}{\"a}n{\"a}nen",
title = "Arithmetical results on certain $q$-series, {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1231--1245",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002663",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002663",
abstract = "As in Part I, entire transcendental solutions of
certain mth order linear q-difference equations are
investigated arithmetically, where now the polynomial
coefficients are much more general. The purpose of this
paper is to produce again lower bounds for the
dimension of the K-vector space generated by 1 and the
values of these solutions at m successive powers of q,
where K is the rational or an imaginary quadratic
field. A new feature in the proof is to use
simultaneously positive and negative powers of q as
interpolation points leading to an extra parameter in
the main result extending its applicability.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2009:COD,
author = "Ping-Shun Chan and Yuval Z. Flicker",
title = "Cyclic Odd Degree Base Change Lifting for Unitary
Groups in Three Variables",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1247--1309",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002687",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002687",
abstract = "Let F be a number field or a $p$-adic field of odd
residual characteristic. Let E be a quadratic extension
of F, and F' an odd degree cyclic field extension of F.
We establish a base-change functorial lifting of
automorphic (respectively, admissible) representations
from the unitary group U(3, E/F) to the unitary group
U(3, F' E/F'). As a consequence, we classify, up to
certain restrictions, the packets of U(3, F' E/F')
which contain irreducible automorphic (respectively,
admissible) representations invariant under the action
of the Galois group Gal(F' E/E). We also determine the
invariance of individual representations. This work is
the first study of base change into an algebraic group
whose packets are not all singletons, and which does
not satisfy the rigidity, or ``strong multiplicity
one'', theorem. Novel phenomena are encountered: e.g.
there are invariant packets where not every irreducible
automorphic (respectively, admissible) member is
Galois-invariant. The restriction that the residual
characteristic of the local fields be odd may be
removed once the multiplicity one theorem for U(3) is
proved to hold unconditionally without restriction on
the dyadic places.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alladi:2009:NCS,
author = "Krishnaswami Alladi",
title = "A new combinatorial study of the {Rogers--Fine}
identity and a related partial theta series",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1311--1320",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002675",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002675",
abstract = "We provide a transparent combinatorial derivation of a
variant of the Rogers--Fine identity and a new
combinatorial proof of a related partial theta
series.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dummigan:2009:SSF,
author = "Neil Dummigan",
title = "Symmetric Square {$L$}-Functions and
{Shafarevich--Tate} Groups, {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "7",
pages = "1321--1345",
month = nov,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002699",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002699",
abstract = "We re-examine some critical values of symmetric square
{$L$}-functions for cusp forms of level one. We
construct some more of the elements of large prime
order in Shafarevich--Tate groups, demanded by the
Bloch--Kato conjecture. For this, we use the Galois
interpretation of Kurokawa-style congruences between
vector-valued Siegel modular forms of genus two (cusp
forms and Klingen--Eisenstein series), making further
use of a construction due to Urban. We must assume that
certain 4-dimensional Galois representations are
symplectic. Our calculations with Fourier expansions
use the Eholzer--Ibukiyama generalization of the
Rankin--Cohen brackets. We also construct some elements
of global torsion which should, according to the
Bloch--Kato conjecture, contribute a factor to the
denominator of the rightmost critical value of the
standard {$L$}-function of the Siegel cusp form. Then
we prove, under certain conditions, that the factor
does occur.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Toulmonde:2009:CAV,
author = "Vincent Toulmonde",
title = "Comportement au voisinage de $1$ de la fonction de
r{\'e}partition de $ \phi (n) / n$. ({French})
[{Behavior} in the neighborhood of $1$ of the partition
function $ \phi (n) / n $]",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1347--1384",
month = dec,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042109001414",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109001414",
abstract = "Let \phi denote Euler's totient function, and G be the
distribution function of \phi (n)/n. Using functional
equations, it is shown that \phi (n)/n is statistically
close to 1 essentially when prime factors of n are
large. A function defined by a difference-differential
equation gives a quantitative measure of the
statistical influence of the size of prime factors of n
on the closeness of \phi (n)/n to 1. As a corollary, an
asymptotic expansion at any order of
G(1)-G(1-\varepsilon) is obtained according to negative
powers of log(1/\varepsilon), when \varepsilon tends to
0$^+$. This improves a result of Erd{\H{o}}s (1946) in
which he gives the first term of it. By optimally
choosing the order of this expansion, an estimation of
G(1)-G(1-\varepsilon) is deduced, involving an error
term of the same size as the best known error term
involved in prime number theorem. Soit \phi
l'indicatrice d'Euler. Nous {\'e}tudions le
comportement au voisinage de 1 de la fonction G de
r{\'e}partition de \phi (n)/n, via la mise en
{\'e}vidence d'{\'e}quations fonctionnelles. Nous
obtenons un r{\'e}sultat mesurant l'influence
statistique de la taille du plus petit facteur premier
d'un entier g{\'e}n{\'e}rique n quant {\`a} la
proximit{\'e} de \phi (n)/n par rapport {\`a} 1. Ce
r{\'e}sultat met en jeu une fonction d{\'e}finie par
une {\'e}quation diff{\'e}rentielle aux
diff{\'e}rences. Nous en d{\'e}duisons un
d{\'e}veloppement limit{\'e} {\`a} tout ordre de
G(1)-G(1-\varepsilon ) selon les puissances de 1/(log
1/\varepsilon), am{\'e}liorant ainsi un r{\'e}sultat
d'Erd{\H{o}}s (1946) dans lequel il obtient le premier
terme de ce d{\'e}veloppement. Une troncature
convenable de ce d{\'e}veloppement fournit un terme
d'erreur comparable {\`a} celui actuellement connu pour
le th{\'e}or{\`e}me des nombres premiers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Berkovich:2009:TPN,
author = "Alexander Berkovich",
title = "The Tri-Pentagonal Number Theorem and Related
Identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1385--1399",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002705",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002705",
abstract = "I revisit an automated proof of Andrews' pentagonal
number theorem found by Riese. I uncover a simple
polynomial identity hidden behind his proof. I explain
how to use this identity to prove Andrews' result along
with a variety of new formulas of similar type. I
reveal an interesting relation between the
tri-pentagonal theorem and items (19), (20), (94), (98)
on the celebrated Slater list. Finally, I establish a
new infinite family of multiple series identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ressler:2009:BQF,
author = "Wendell Ressler",
title = "On Binary Quadratic Forms and the {Hecke} Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1401--1418",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002730",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002730",
abstract = "We present a reduction theory for certain binary
quadratic forms with coefficients in
{\mathbb{Z}}[\lambda ], where \lambda is the minimal
translation in a Hecke group. We generalize from the
modular group \Gamma (1) = PSL(2,{\mathbb{Z}}) to the
Hecke groups and make extensive use of modified
negative continued fractions. We also define and
characterize ``reduced'' and ``simple'' hyperbolic
fixed points of the Hecke groups.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bell:2009:BSF,
author = "Jason P. Bell and Jonathan W. Bober",
title = "Bounded Step Functions and Factorial Ratio Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1419--1431",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002742",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002742",
abstract = "We study certain step functions whose nonnegativity is
related to the integrality of sequences of ratios of
factorial products. In particular, we obtain a lower
bound for the mean square of such step functions which
allows us to give a restriction on when such a
factorial ratio sequence can be integral. Additionally,
we note that this work has applications to the
classification of cyclic quotient singularities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{El-Guindy:2009:FEM,
author = "Ahmad El-Guindy",
title = "{Fourier} Expansions with Modular Form Coefficients",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1433--1446",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002717",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002717",
abstract = "In this paper, we study the Fourier expansion where
the coefficients are given as the evaluation of a
sequence of modular forms at a fixed point in the upper
half-plane. We show that for prime levels l for which
the modular curve X$_0$ (l) is hyperelliptic (with
hyperelliptic involution of the Atkin--Lehner type)
then one can choose a sequence of weight k (any even
integer) forms so that the resulting Fourier expansion
is itself a meromorphic modular form of weight 2-k.
These sequences have many interesting properties, for
instance, the sequence of their first nonzero
next-to-leading coefficient is equal to the terms in
the Fourier expansion of a certain weight 2-k form. The
results in the paper generalizes earlier work by Asai,
Kaneko, and Ninomiya (for level one), and Ahlgren (for
the cases where X$_0$ (l) has genus zero).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ehrenpreis:2009:EPS,
author = "Leon Ehrenpreis",
title = "{Eisenstein} and {Poincar{\'e}} Series on {$ \mathrm
{SL}(3, r) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1447--1475",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002729",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002729",
abstract = "This work continues the ideas presented in the
author's book, {\em The Universality of the Radon
Transform\/} (Oxford, 2003), which deals with the group
SL(2,R). The complication that arises for G = SL(3,R)
comes from the fact that there are now two fundamental
representations. This has the consequence that the wave
operator, which plays a central role in our work on
SL(2,R) is replaced by an overdetermined system of
partial differential equations. The analog of the wave
operator is defined using an MN invariant orbit of G
acting on the direct sum of the symmetric squares of
the fundamental representations. The relation of
orbits, or, in general, of any algebraic variety, to a
system of partial differential equations comes via the
Fundamental Principle, which shows how Fourier
transforms of functions or measures on an algebraic
variety correspond to solutions of the system of
partial differential equations defined by the equations
of the variety. In particular, we can start with the
sum T of the delta functions of the orbit of the group
\Gamma = SL(2,Z) on the light cone. We then take its
Fourier transform, using a suitable quadratic form. We
then decompose the Fourier transform under the
commuting group of G. In this way, we obtain a \Gamma
invariant distribution which has a natural restriction
to the orbit G/K, which is the symmetric space of G.
This restriction is (essentially) the nonanalytic
Eisenstein series. We can compute the periods of the
Eisenstein series over various orbits of subgroups of G
by means of the Euclidean Plancherel formula. A more
complicated form of these ideas is needed to define
Poincar{\'e} series.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2009:SFT,
author = "Zhi-Guo Liu and Xiao-Mei Yang",
title = "On the {Schr{\"o}ter} formula for theta functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1477--1488",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002754",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002754",
abstract = "The Schr{\"o}ter formula is an important theta
function identity. In this paper, we will point out
that some well-known addition formulas for theta
functions are special cases of the Schr{\"o}ter
formula. We further show that the Hirschhorn septuple
product identity can also be derived from this formula.
In addition, this formula allows us to derive four
remarkable theta functions identities, two of them are
extensions of two well-known Ramanujan's identities
related to the modular equations of degree 5. A
trigonometric identity is also proved.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2009:AIV,
author = "Anonymous",
title = "Author Index (Volume 5)",
journal = j-INT-J-NUMBER-THEORY,
volume = "5",
number = "8",
pages = "1489--1493",
month = dec,
year = "2009",
DOI = "https://doi.org/10.1142/S1793042109002766",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042109002766",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baoulina:2010:NSC,
author = "Ioulia Baoulina",
title = "On the Number of Solutions to Certain Diagonal
Equations Over Finite Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "1--14",
month = feb,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110002776",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002776",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Munshi:2010:DPR,
author = "Ritabrata Munshi",
title = "Density of Positive Rank Fibers in Elliptic
Fibrations, {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "15--23",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002867",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002867",
abstract = "We show that for a quartic elliptic fibration over a
real number field, existence of two positive rank
fibers implies existence of a dense set of positive
rank fibers. We also prove the same result for certain
sextic families.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Krieg:2010:TSH,
author = "Aloys Krieg",
title = "Theta Series Over the {Hurwitz} Quaternions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "25--36",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002788",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002788",
abstract = "There are six theta constants over the Hurwitz
quaternions on the quaternion half-space of degree 2.
The paper describes the behavior of these theta
constants under the transpose mapping, which can be
derived from the Fourier expansions. The results are
applied to the theta series of the first and second
kind.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alaca:2010:FOQ,
author = "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Kenneth S.
Williams",
title = "Fourteen Octonary Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "37--50",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000279X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000279X",
abstract = "We use the recent evaluation of certain convolution
sums involving the sum of divisors function to
determine the number of representations of a positive
integer by certain diagonal octonary quadratic forms
whose coefficients are 1, 2 or 4.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Beck:2010:FTC,
author = "Matthias Beck and Mary Halloran",
title = "Finite Trigonometric Character Sums Via Discrete
{Fourier} Analysis",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "51--67",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002806",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002806",
abstract = "We prove several old and new theorems about finite
sums involving characters and trigonometric functions.
These sums can be traced back to theta function
identities from Ramanujan's notebooks and were first
systematically studied by Berndt and Zaharescu where
their proofs involved complex contour integration. We
show how to prove most of Berndt--Zaharescu's and some
new identities by elementary methods of discrete
Fourier analysis.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Miller:2010:ATN,
author = "Alison Miller and Aaron Pixton",
title = "Arithmetic Traces of Non-Holomorphic Modular
Invariants",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "69--87",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002818",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002818",
abstract = "We extend results of Bringmann and Ono that relate
certain generalized traces of Maass--Poincar{\'e}
series to Fourier coefficients of modular forms of
half-integral weight. By specializing to cases in which
these traces are usual traces of algebraic numbers, we
generalize results of Zagier describing arithmetic
traces associated to modular forms. We define
correspondences and. We show that if f is a modular
form of non-positive weight 2 - 2 \lambda and odd level
N, holomorphic away from the cusp at infinity, then the
traces of values at Heegner points of a certain
iterated non-holomorphic derivative of f are equal to
Fourier coefficients of the half-integral weight
modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2010:CSA,
author = "Heng Huat Chan and Shaun Cooper and Francesco Sica",
title = "Congruences Satisfied by {Ap{\'e}ry}-Like Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "89--97",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002879",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002879",
abstract = "In this article, we investigate congruences satisfied
by Ap{\'e}ry-like numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hassen:2010:HZF,
author = "Abdul Hassen and Hieu D. Nguyen",
title = "Hypergeometric Zeta Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "99--126",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000282X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000282X",
abstract = "This paper investigates a new family of special
functions referred to as hypergeometric zeta functions.
Derived from the integral representation of the
classical Riemann zeta function, hypergeometric zeta
functions exhibit many properties analogous to their
classical counterpart, including the intimate
connection to Bernoulli numbers. These new properties
are treated in detail and are used to demonstrate a
functional inequality satisfied by second-order
hypergeometric zeta functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kane:2010:RIT,
author = "Ben Kane",
title = "Representations of Integers by Ternary Quadratic
Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "127--158",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002831",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002831",
abstract = "We investigate the representation of integers by
quadratic forms whose theta series lie in Kohnen's plus
space, where p is a prime. Conditional upon certain GRH
hypotheses, we show effectively that every sufficiently
large discriminant with bounded divisibility by p is
represented by the form, up to local conditions. We
give an algorithm for explicitly calculating the
bounds. For small p, we then use a computer to find the
full list of all discriminants not represented by the
form. Finally, conditional upon GRH for {$L$}-functions
of weight 2 newforms, we give an algorithm for
computing the implied constant of the
Ramanujan--Petersson conjecture for weight 3/2 cusp
forms of level 4N in Kohnen's plus space with N odd and
squarefree.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
%% Check page gap at publisher site: v6 n1 pp159--160
@Article{Bremner:2010:CST,
author = "Andrew Bremner and Blair K. Spearman",
title = "Cyclic sextic trinomials {$ x^6 + A x + B $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "161--167",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002843",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002843",
abstract = "A correspondence is obtained between irreducible
cyclic sextic trinomials x$^6$ + Ax + B \in {$ \mathbb
{Q}$}[x] and rational points on a genus two curve. This
implies that up to scaling, x$^6$ + 133x + 209 is the
only cyclic sextic trinomial of the given type.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alaca:2010:SQF,
author = "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Kenneth S.
Williams",
title = "Sextenary Quadratic Forms and an Identity of {Klein}
and {Fricke}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "169--183",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002880",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002880",
abstract = "Formulae, originally conjectured by Liouville, are
proved for the number of representations of a positive
integer n by each of the eight sextenary quadratic
forms, , , , , , , .",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Boylan:2010:APC,
author = "Matthew Boylan",
title = "Arithmetic Properties of Certain Level One {Mock}
Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "185--202",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002855",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002855",
abstract = "In a recent work, Bringmann and Ono [4] show that
Ramanujan's f(q) mock theta function is the holomorphic
projection of a harmonic weak Maass form of weight 1/2.
In this paper, we extend the work of Ono in [13]. In
particular, we study holomorphic projections of certain
integer weight harmonic weak Maass forms on SL$_2$
({\mathbb{Z}}) using Hecke operators and the
differential theta-operator.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Copil:2010:RCP,
author = "Vlad Copil and Lauren{\c{t}}iu Panaitopol",
title = "On the Ratio of Consecutive Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "203--210",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002934",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002934",
abstract = "For n \geq 1, let p$_n$ be the nth prime number and
for n \geq 1. Using several results of Erd{\H{o}}s, we
study the sequence (q$_n$)$_{n \geq 1}$ and we prove
similar results as for the sequence (d$_n$)$_{n \geq
1}$, d$_n$ = p$_{n + 1}$- p$_n$. We also consider the
sequence for n \geq 1 and denote by G$_n$ and A$_n$ its
geometrical and arithmetical averages. We prove that
for n \geq 4.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Coons:2010:TSR,
author = "Michael Coons",
title = "The Transcendence of Series Related to {Stern}'s
Diatomic Sequence",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "1",
pages = "211--217",
month = feb,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002958",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:21 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002958",
abstract = "We prove various transcendence results regarding the
Stern sequence and related functions; in particular, we
prove that the generating function of the Stern
sequence is transcendental. Transcendence results are
also proven for the generating function of the Stern
polynomials and for power series whose coefficients
arise from some special subsequences of Stern's
sequence.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lagarias:2010:CSS,
author = "Jeffrey C. Lagarias",
title = "Cyclic Systems of Simultaneous Congruences",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "219--245",
month = mar,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110002892",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See erratum \cite{Lagarias:2010:ECS}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002892",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kim:2010:BPQ,
author = "Sun Kim",
title = "A Bijective Proof of the Quintuple Product Identity",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "247--256",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002909",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002909",
abstract = "We give a bijective proof of the quintuple product
identity using bijective proofs of Jacobi's triple
product identity and Euler's recurrence relation.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bouallegue:2010:KNS,
author = "Kais Bouall{\`e}gue and Othman Echi and Richard G. E.
Pinch",
title = "{Korselt} Numbers and Sets",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "257--269",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002922",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002922",
abstract = "Let $ \alpha \in \mathbb {Z} \setminus {0} $. A
positive integer $N$ is said to be an $ \alpha
$-Korselt number ($ K_{\alpha }$-number, for short) if
$ N \neq \alpha $ and $ p \alpha $ divides $ N - \alpha
$ for each prime divisor $p$ of $N$. We are concerned,
here, with both a numerical and theoretical study of
composite squarefree Korselt numbers. The paper
contains two main results. The first one shows that for
$ \alpha \in \mathbb {Z} \setminus {0}$, the following
properties hold: (i) If $ \alpha \leq 1$, then each
composite squarefree $ K_{\alpha }$-number has at least
three prime factors. (ii) Suppose that $ \alpha > 1$.
Let $ p < q$ be two prime numbers and $ N \coloneq p
q$. If $N$ is an \alpha Korselt number, then $ p < q
\leq 4 \alpha - 3$. In particular, there are only
finitely many $ \alpha $ Korselt numbers with exactly
two prime factors. Let $ \alpha \in \mathbb {N}
\setminus {0}$; by an $ \alpha $-Williams number ($
W_{\alpha }$-number, for short) we mean a positive
integer which is both a $ K_{\alpha }$-number and a $
K_{- \alpha }$-number. Our second main result shows
that if $p$, $ 3 p - 2 $, $ 3 p + 2$ are all prime,
then their product is a ($ 3 p$)-Williams number.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kelmer:2010:DTK,
author = "Dubi Kelmer",
title = "Distribution of Twisted {Kloosterman} Sums Modulo
Prime Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "271--280",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002910",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002910",
abstract = "In this paper, we study Kloosterman sums twisted by
multiplicative characters modulo a prime power. We
show, by an elementary calculation, that these sums
become equidistributed on the real line with respect to
a suitable measure.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Garvan:2010:CAS,
author = "F. G. Garvan",
title = "Congruences for {Andrews}' Smallest Parts Partition
Function and New Congruences for {Dyson}'s Rank",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "281--309",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000296X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000296X",
abstract = "Let spt(n) denote the total number of appearances of
smallest parts in the partitions of n. Recently,
Andrews showed how spt(n) is related to the second rank
moment, and proved some surprising Ramanujan-type
congruences mod 5, 7 and 13. We prove a generalization
of these congruences using known relations between rank
and crank moments. We obtain explicit Ramanujan-type
congruences for spt(n) mod \ell for \ell = 11, 17, 19,
29, 31 and 37. Recently, Bringmann and Ono proved that
Dyson's rank function has infinitely many
Ramanujan-type congruences. Their proof is
non-constructive and utilizes the theory of weak Maass
forms. We construct two explicit nontrivial examples
mod 11 using elementary congruences between rank
moments and half-integer weight Hecke eigenforms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bennett:2010:DE,
author = "Michael A. Bennett and Jordan S. Ellenberg and Nathan
C. Ng",
title = "The {Diophantine} equation {$ A^4 + 2^\delta B^2 = C^n
$}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "311--338",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002971",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002971",
abstract = "In a previous paper, the second author proved that the
equation $ A^4 + B^2 = C^p $ had no integral solutions
for prime $ p > 211 $ and $ (A, B, C) = 1 $. In the
present paper, we explain how to extend this result to
smaller exponents, and to the related equation $ A^4 +
2 B^2 = C^p $.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Souderes:2010:MDS,
author = "Ismael Soud{\`e}res",
title = "{Motivic} Double Shuffle",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "339--370",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002995",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002995",
abstract = "The goal of this paper is to give an elementary proof
of the double shuffle relations directly for the
Goncharov and Manin motivic multiple zeta values. The
shuffle relation is straightforward, but for the
stuffle, we use a modification of a method first
introduced by Cartier for the purpose of proving
stuffle for the real multiple zeta values. We will use
both the representation of multiple zeta values on the
moduli spaces of curve introduced by Goncharov and
Manin and we will apply suitable blow-up sequences to
the representation of multiple zeta values as integral
over a cube.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Han:2010:FNP,
author = "Jeong Soon Han and Hee Sik Kim and J. Neggers",
title = "The {Fibonacci}-Norm of a Positive Integer:
Observations and Conjectures",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "371--385",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003009",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See acknowledgement of priority \cite{Han:2011:APF}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003009",
abstract = "In this paper, we define the Fibonacci-norm of a
natural number n to be the smallest integer k such that
n|F$_k$, the kth Fibonacci number. We show that for m
\geq 5. Thus by analogy we say that a natural number n
\geq 5 is a local-Fibonacci-number whenever . We offer
several conjectures concerning the distribution of
local-Fibonacci-numbers. We show that, where provided
F$_{m + k}$ \equiv F$_m$ (mod n) for all natural
numbers m, with k \geq 1 the smallest natural number
for which this is true.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nebe:2010:LDS,
author = "Gabriele Nebe and Boris Venkov",
title = "Low-Dimensional Strongly Perfect Lattices. {III}: Dual
Strongly Perfect Lattices of Dimension $ 14 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "387--409",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003022",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003022",
abstract = "A lattice is called dual strongly perfect if both, the
lattice and its dual, are strongly perfect. We show
that the extremal 3-modular lattice [\pm G$_2$
(3)]$_{14}$ with automorphism group C$_2$ $ \times $
G$_2$ ({$ \mathbb {F} $}$_3$) is the unique dual
strongly perfect lattice of dimension 14.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vulakh:2010:MBI,
author = "L. Ya. Vulakh",
title = "Minima of Binary Indefinite {Hermitian} Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "411--435",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003034",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003034",
abstract = "Classification of binary indefinite primitive
Hermitian forms modulo the action of the extended
Bianchi group (or Hilbert modular group) B$_d$ is
given. When the discriminant of the quadratic field
(and d) is negative, the results obtained can be
applied to classify the maximal non-elementary Fuchsian
subgroups of B$_d$, and to find the Hermitian points in
the Markov spectrum of B$_d$. If \nu is a Hermitian
point in the spectrum, then there is a set of extremal
geodesics in H$^3$, the upper half-space model of the
three-dimensional hyperbolic space, with diameter
1/\nu, which depends on one continuous parameter.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhao:2010:EDP,
author = "Yusheng Zhao and Wei Li and Xianke Zhang",
title = "Effective Determination of Prime Decompositions of
Cubic Function Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "437--448",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110002983",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002983",
abstract = "In this paper, we determine completely the prime
decomposition of cubic function fields by effective and
explicit methods.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kim:2010:CPC,
author = "Byungchan Kim",
title = "Combinatorial Proofs of Certain Identities Involving
Partial Theta Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "2",
pages = "449--460",
month = mar,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003046",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003046",
abstract = "In this brief note, we give combinatorial proofs of
two identities involving partial theta functions. As an
application, we prove an identity for the product of
partial theta functions, first established by Andrews
and Warnaar. We also provide a generalization of the
first two identities and give a combinatorial proof of
the generalized identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{McCarthy:2010:HSP,
author = "Dermot McCarthy",
title = "{$_3 F_2$} Hypergeometric Series and Periods of
Elliptic Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "461--470",
month = may,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110002946",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110002946",
abstract = "We express the real period of a family of elliptic
curves in terms of classical hypergeometric series.
This expression is analogous to a result of Ono which
relates the trace of Frobenius of the same family of
elliptic curves to a Gaussian hypergeometric series.
This analogy provides further evidence of the interplay
between classical and Gaussian hypergeometric series.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Viada:2010:LBN,
author = "Evelina Viada",
title = "Lower Bounds for the Normalized Height and Non-Dense
Subsets of Subvarieties of {Abelian} Varieties",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "471--499",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003010",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003010",
abstract = "This work is the third part of a series of papers. In
the first two, we considered curves and varieties in a
power of an elliptic curve. Here, we deal with
subvarieties of an abelian variety in general. Let V be
a proper irreducible subvariety of dimension d in an
abelian variety A, both defined over the algebraic
numbers. We say that V is weak-transverse if V is not
contained in any proper algebraic subgroup of A, and
transverse if it is not contained in any translate of
such a subgroup. Assume a conjectural lower bound for
the normalized height of V. Then, for V transverse, we
prove that the algebraic points of bounded height of V
which lie in the union of all algebraic subgroups of A
of codimension at least d + 1 translated by the points
close to a subgroup \Gamma of finite rank, are
non-Zariski-dense in V. If \Gamma has rank zero, it is
sufficient to assume that V is weak-transverse. The
notion of closeness is defined using a height
function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Borwein:2010:DTM,
author = "Jonathan M. Borwein and O-Yeat Chan",
title = "Duality in tails of multiple-zeta values",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "501--514",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003058",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11M32 (33C20 33F05)",
MRnumber = "2652893",
MRreviewer = "Zhonghua Li",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "http://docserver.carma.newcastle.edu.au/1218/;
https://www.worldscientific.com/doi/10.1142/S1793042110003058",
abstract = "Duality relations are deduced for tails of
multiple-zeta values using elementary methods. These
formulas extend the classical duality formulas for
multiple-zeta values.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2010:DTM",
}
@Article{Chu:2010:BBL,
author = "Wenchang Chu and Wenlong Zhang",
title = "Bilateral {Bailey} Lemma and False Theta Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "515--577",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000306X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000306X",
abstract = "By examining the transformation formulae between
unilateral series and bilateral ones derived from the
bilateral Bailey lemma, we establish numerous
identities of false theta functions, including most of
the known ones discovered mainly by Rogers [40] and
Ramanujan in his \booktitle{Lost Notebook} [39].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fehm:2010:RAV,
author = "Arno Fehm and Sebastian Petersen",
title = "On the Rank of {Abelian} Varieties Over Ample Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "579--586",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003071",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003071",
abstract = "A field K is called ample if every smooth K-curve that
has a K-rational point has infinitely many of them. We
prove two theorems to support the following conjecture,
which is inspired by classical infinite rank results:
Every non-zero Abelian variety A over an ample field K
which is not algebraic over a finite field has infinite
rank. First, the {\mathbb{Z}}$_{(p)}$-module A(K)
\otimes {\mathbb{Z}}$_{(p)}$ is not finitely generated,
where p is the characteristic of K. In particular, the
conjecture holds for fields of characteristic zero.
Second, if K is an infinite finitely generated field
and S is a finite set of local primes of K, then every
Abelian variety over K acquires infinite rank over
certain subfields of the maximal totally S-adic Galois
extension of K. This strengthens a recent infinite rank
result of Geyer and Jarden.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bugeaud:2010:PRS,
author = "Yann Bugeaud and Maurice Mignotte",
title = "Polynomial Root Separation",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "587--602",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003083",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003083",
abstract = "We discuss the following question: How close to each
other can two distinct roots of an integer polynomial
be? We summarize what is presently known on this and
related problems, and establish several new results on
root separation of monic, integer polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ruhl:2010:AIQ,
author = "Klaas-Tido R{\"u}hl",
title = "Annihilating Ideals of Quadratic Forms Over Local and
Global Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "603--624",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003095",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003095",
abstract = "We study annihilating polynomials and annihilating
ideals for elements of Witt rings for groups of
exponent 2. With the help of these results and certain
calculations involving the Clifford invariant, we are
able to give full sets of generators for the
annihilating ideal of both the isometry class and the
equivalence class of an arbitrary quadratic form over a
local field. By applying the Hasse--Minkowski theorem,
we can then achieve the same for an arbitrary quadratic
form over a global field.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Le:2010:APT,
author = "Daniel Le and Shelly Manber and Shrenik Shah",
title = "On $p$-adic properties of twisted traces of singular
moduli",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "625--653",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003101",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003101",
abstract = "We prove that logarithmic derivatives of certain
twisted Hilbert class polynomials are holomorphic
modular forms modulo p of filtration p + 1. We derive
$p$-adic information about twisted Hecke traces and
Hilbert class polynomials. In this framework, we
formulate a precise criterion for $p$-divisibility of
class numbers of imaginary quadratic fields in terms of
the existence of certain cusp forms modulo p. We
explain the existence of infinite classes of congruent
twisted Hecke traces with fixed discriminant in terms
of the factorization of the associated Hilbert class
polynomial modulo p. Finally, we provide a new proof of
a theorem of Ogg classifying those p for which all
supersingular j-invariants modulo p lie in F$_p$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Haynes:2010:NDN,
author = "Alan K. Haynes",
title = "Numerators of Differences of Nonconsecutive {Farey}
Fractions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "655--666",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003113",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003113",
abstract = "An elementary but useful fact is that the numerator of
the difference of two consecutive Farey fractions is
equal to one. For triples of consecutive fractions, the
numerators of the differences are well understood and
have applications to several interesting problems. In
this paper, we investigate numerators of differences of
fractions which are farther apart. We establish
algebraic identities between such differences which
then allow us to calculate their average values by
using properties of a measure preserving transformation
of the Farey triangle.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Witno:2010:EPP,
author = "Amin Witno",
title = "On Elite Primes of Period Four",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "667--671",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003149",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003149",
abstract = "A prime p is elite if all sufficiently large Fermat
numbers F$_n$ = 2$^{2 n}$ + 1 are quadratic nonresidues
modulo p. In contrast, p is anti-elite if all
sufficiently large F$_n$ are quadratic residues modulo
p. The sequence F$_n$ modulo p is necessarily periodic.
We give a sequence of pairwise coprime integers whose
prime factors are each elite or anti-elite with period
four.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2010:RCCa,
author = "Hei-Chi Chan",
title = "{Ramanujan}'s cubic continued fraction and an analog
of his ``{Most Beautiful Identity}''",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "673--680",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003150",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003150",
abstract = "In this paper, we prove an analog of Ramanujan's
``Most Beautiful Identity''. This analog is closely
related to Ramanujan's beautiful results involving the
cubic continued fraction.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chao:2010:NBS,
author = "Kuok Fai Chao and Roger Plymen",
title = "A new bound for the smallest $x$ with $ \pi (x) > \li
(x)$",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "681--690",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003125",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003125",
abstract = "We reduce the leading term in Lehman's theorem. This
improved estimate allows us to refine the main theorem
of Bays and Hudson [2]. Entering 2,000,000 Riemann
zeros, we prove that there exists x in the interval
[exp (727.951858), exp (727.952178)] for which \pi (x)
- li(x) > 3.2 $ \times $ 10$^{151}$. There are at least
10$^{154}$ successive integers x in this interval for
which \pi (x) > li(x). This interval is strictly a
sub-interval of the interval in Bays and Hudson, and is
narrower by a factor of about 12.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kida:2010:CBQ,
author = "Masanari Kida and Y{\=u}ichi Rikuna and Atsushi Sato",
title = "Classifying {Brumer}'s Quintic Polynomials by Weak
{Mordell--Weil} Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "691--704",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003162",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003162",
abstract = "We develop a general classification theory for
Brumer's dihedral quintic polynomials by means of
Kummer theory arising from certain elliptic curves. We
also give a similar theory for cubic polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lalin:2010:CB,
author = "Matilde N. Lal{\'i}n",
title = "On a Conjecture by {Boyd}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "705--711",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003174",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003174",
abstract = "The aim of this note is to prove the Mahler measure
identity m(x + x$^{-1}$ + y + y$^{-1}$ + 5) = 6m(x +
x$^{-1}$ + y + y$^{-1}$ + 1) which was conjectured by
Boyd. The proof is achieved by proving relationships
between regulators of both curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vulakh:2010:HPM,
author = "L. Ya Vulakh",
title = "{Hermitian} Points in {Markov} Spectra",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "713--730",
month = jun,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110003186",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003186",
abstract = "Let H$^n$ be the upper half-space model of the
n-dimensional hyperbolic space. For n=3, Hermitian
points in the Markov spectrum of the extended Bianchi
group B$_d$ are introduced for any d. If \nu is a
Hermitian point in the spectrum, then there is a set of
extremal geodesics in H$^3$ with diameter 1/\nu, which
depends on one continuous parameter. It is shown that
\nu$^2$ \leq |D|/24 for any imaginary quadratic field
with discriminant D, whose ideal-class group contains
no cyclic subgroup of order 4, and in many other cases.
Similarly, in the case of n = 4, if \nu is a Hermitian
point in the Markov spectrum for SV(Z$^4$), some
discrete group of isometries of H$^4$, then the
corresponding set of extremal geodesics depends on two
continuous parameters.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vulakh:2010:DAI,
author = "L. Ya. Vulakh",
title = "{Diophantine} Approximation in Imaginary Quadratic
Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "731--766",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003137",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003137",
abstract = "Let H$^3$ be the upper half-space model of the
three-dimensional hyperbolic space. For certain
cocompact Fuchsian subgroups \Gamma of an extended
Bianchi group B$_d$, the extremality of the axis of
hyperbolic F \in \Gamma in H$_3$ with respect to \Gamma
implies its extremality with respect to B$_d$. This
reduction is used to obtain sharp lower bounds for the
Hurwitz constants and lower bounds for the highest
limit points in the Markov spectra of B$_d$ for some d
< 1000. In particular, such bounds are found for all
non-Euclidean class one imaginary quadratic fields. The
Hurwitz constants for the imaginary quadratic fields
with discriminants -120 and -132 are given. The second
minima are also indicated for these fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ganguly:2010:DSC,
author = "Satadal Ganguly",
title = "On the Dimension of the Space of Cusp Forms of
Octahedral Type",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "767--783",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003198",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003198",
abstract = "For a prime q \equiv 3 (mod 4) and the character, we
consider the subspace of the space of holomorphic cusp
forms of weight one, level q and character \chi that is
spanned by forms that correspond to Galois
representations of octahedral type. We prove that this
subspace has dimension bounded by upto multiplication
by a constant that depends only on \varepsilon.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rowell:2010:NEL,
author = "Michael Rowell",
title = "A New Exploration of the {Lebesgue} Identity",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "785--798",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003204",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003204",
abstract = "We introduce a new combinatorial proof of the Lebesgue
identity which allows us to find a new finite form of
the identity. Using this new finite form we are able to
make new observations about special cases of the
Lebesgue identity, namely the ``little'' G{\"o}llnitz
theorems and Sylvester's identity.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lev:2010:ABA,
author = "Vsevolod F. Lev and Mikhail E. Muzychuk and Rom
Pinchasi",
title = "Additive Bases in {Abelian} Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "799--809",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003216",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003216",
abstract = "Let G be a finite, non-trivial Abelian group of
exponent m, and suppose that B$_1$, \ldots, B$_k$ are
generating subsets of G. We prove that if k > 2m ln
log$_2$ |G|, then the multiset union B$_1$ \cup B$_k$
forms an additive basis of G; that is, for every g \in
G, there exist A$_1$ \subseteq B$_1$, \ldots, A$_k$
\subseteq B$_k$ such that. This generalizes a result of
Alon, Linial and Meshulam on the additive bases
conjecture. As another step towards proving the
conjecture, in the case where B$_1$, \ldots, B$_k$ are
finite subsets of a vector space, we obtain lower-bound
estimates for the number of distinct values, attained
by the sums of the form, where A$_i$ vary over all
subsets of B$_i$ for each i = 1,\ldots, k. Finally, we
establish a surprising relation between the additive
bases conjecture and the problem of covering the
vertices of a unit cube by translates of a lattice, and
present a reformulation of (the strong form of) the
conjecture in terms of coverings.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Volkov:2010:ASS,
author = "Maja Volkov",
title = "{Abelian} Surfaces with Supersingular Good Reduction
and Non-Semisimple {Tate} Module",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "811--818",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003228",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003228",
abstract = "We show the existence of abelian surfaces over {$
\mathbb {Q} $}$_p$ having good reduction with
supersingular special fiber whose associated $p$-adic
Galois module is not semisimple.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2010:RCCb,
author = "Hei-Chi Chan",
title = "{Ramanujan}'s Cubic Continued Fraction and {Ramanujan}
Type Congruences for a Certain Partition Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "819--834",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003241",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003241",
abstract = "In this paper, we study the divisibility of the
function a(n) defined by. In particular, we prove
certain ``Ramanujan type congruences'' for a(n) modulo
powers of 3.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sinick:2010:RCC,
author = "Jonah Sinick",
title = "{Ramanujan} Congruences for a Class of Eta Quotients",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "835--847",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003253",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003253",
abstract = "We consider a class of generating functions analogous
to the generating function of the partition function
and establish a bound on the primes \ell for which
their coefficients c(n) obey congruences of the form
c(\ell n + a) \equiv 0 (mod \ell). We apply this result
to obtain a complete characterization of the
congruences of the same form that the sequences c$_N$
(n) satisfy, where c$_N$ (n) is defined by. This last
result answers a question of H.-C. Chan.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Xia:2010:BNC,
author = "Binzhou Xia and Tianxin Cai",
title = "{Bernoulli} Numbers and Congruences for Harmonic
Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "849--855",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003265",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003265",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Brown:2010:FNH,
author = "Jim Brown",
title = "The first negative {Hecke} eigenvalue of genus $2$
{Siegel} cuspforms with level $ n \geq 1$",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "857--867",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003277",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003277",
abstract = "In this short paper, we extend results of Kohnen and
Sengupta on the sign of eigenvalues of Siegel
cuspforms. We show that their bound for the first
negative Hecke eigenvalue of a genus 2 Siegel cuspform
of level 1 extends to the case of level N > 1. We also
discuss the signs of Hecke eigenvalues of CAP forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Williams:2010:UIC,
author = "Gerald Williams",
title = "Unimodular Integer Circulants Associated with
Trinomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "869--876",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003289",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003289",
abstract = "The n $ \times $ n circulant matrix associated with
the polynomial (with d < n) is the one with first row
(a$_0$ \cdots a$_d$ 0 \cdots 0). The problem as to when
such circulants are unimodular arises in the theory of
cyclically presented groups and leads to the following
question, previously studied by Odoni and Cremona: when
is Res(f(t), t$^n$-1) = \pm 1? We give a complete
answer to this question for trinomials f(t) = t$^m$ \pm
t$^k$ \pm 1. Our main result was conjectured by the
author in an earlier paper and (with two exceptions)
implies the classification of the finite
Cavicchioli--Hegenbarth--Repov{\v{s}} generalized
Fibonacci groups, thus giving an almost complete answer
to a question of Bardakov and Vesnin.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ahmadi:2010:MOG,
author = "Omran Ahmadi and Igor E. Shparlinski and Jos{\'e}
Felipe Voloch",
title = "Multiplicative Order of {Gauss} Periods",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "877--882",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003290",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003290",
abstract = "We obtain a lower bound on the multiplicative order of
Gauss periods which generate normal bases over finite
fields. This bound improves the previous bound of von
zur Gathen and Shparlinski.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Balazard:2010:CBD,
author = "Michel Balazard and Anne {De Roton}",
title = "Sur un crit{\`e}re de {B{\'a}ez--Duarte} pour
l'hypoth{\`e}se de {Riemann}. ({French}) [{On} a
criterion of {B{\'a}ez--Duarte} for the {Riemann
Hypothesis}]",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "883--903",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003307",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003307",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Maier:2010:ESP,
author = "H. Maier and A. Sankaranarayanan",
title = "Exponential Sums Over Primes in Residue Classes",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "905--918",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003319",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003319",
abstract = "We specialize a problem studied by Elliott, the
behavior of arbitrary sequences a$_p$ of complex
numbers on residue classes to prime moduli to the case
a$_p$ = e(\alpha p). For these special cases, we obtain
under certain additional conditions improvements on
Elliott's results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Roy:2010:SVE,
author = "Damien Roy",
title = "Small Value Estimates for the Additive Group",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "919--956",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000323X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000323X",
abstract = "We generalize Gel'fond's criterion for algebraic
independence to the context of a sequence of
polynomials whose first derivatives take small values
on large subsets of a fixed subgroup of $ \mathbb {C}
$, instead of just one point (one extension deals with
a subgroup of $ \mathbb {C}^\times $).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lagarias:2010:ECS,
author = "Jeffrey C. Lagarias",
title = "Erratum: {``Cyclic Systems of Simultaneous
Congruences''}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "4",
pages = "??--??",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003320",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:22 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See \cite{Lagarias:2010:CSS}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003320",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jouhet:2010:IEI,
author = "Fr{\'e}d{\'e}ric Jouhet and Elie Mosaki",
title = "Irrationalit{\'e} aux entiers impairs positifs d'un
$q$-analogue de la fonction z{\^e}ta de {Riemann}.
({French}) [{Irrationality} to positive odd integers of
a $q$-analogue of the {Riemann} zeta function]",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "959--988",
month = aug,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110003332",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003332",
abstract = "Dans cet article, nous nous int{\'e}ressons {\`a} un
q-analogue aux entiers positifs de la fonction z{\^e}ta
de Riemann, que l'on peut {\'e}crire pour s \in
\mathbb{N} * sous la forme \zeta$_q$ (s) = $ \sum_{k
\geq 1}$ q$^k$ $ \sum_{d|k}$ d$^{s - 1}$. Nous donnons
une nouvelle minoration de la dimension de l'espace
vectoriel sur {$ \mathbb {Q}$} engendr{\'e}, pour 1/q
\in {\mathbb{Z}}{-1; 1} et A entier pair, par 1,
\zeta$_q$ (3), \zeta$_q$ (5), \ldots, \zeta$_q$ (A -
1). Ceci am{\'e}liore un r{\'e}sultat r{\'e}cent de
Krattenthaler, Rivoal et Zudilin ([13]). En particulier
notre r{\'e}sultat a pour cons{\'e}quence le fait que
pour 1/q \in {\mathbb{Z}}{-1; 1}, au moins l'un des
nombres \zeta$_q$ (3), \zeta$_q$ (5), \zeta$_q$ (7),
\zeta$_q$ (9) est irrationnel. In this paper, we focus
on a q-analogue of the Riemann zeta function at
positive integers, which can be written for s \in
\mathbb{N} * by \zeta$_q$ (s) = $ \sum_{k \geq 1}$
q$^k$ $ \sum_{d|k}$ d$^{s - 1}$. We give a new lower
bound for the dimension of the vector space over {$
\mathbb {Q}$} spanned, for 1/q \in {\mathbb{Z}}{-1; 1}
and an even integer A, by 1, \zeta$_q$ (3), \zeta$_q$
(5), \ldots, \zeta$_q$ (A-1). This improves a recent
result of Krattenthaler, Rivoal and Zudilin ([13]). In
particular, a consequence of our result is that for 1/q
\in {\mathbb{Z}}{-1; 1}, at least one of the numbers
\zeta$_q$ (3), \zeta$_q$ (5), \zeta$_q$ (7), \zeta$_q$
(9) is irrational.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Hasegawa:2010:AOT,
author = "Takehiro Hasegawa",
title = "On Asymptotically Optimal Towers Over Quadratic Fields
Related to {Gauss} Hypergeometric Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "989--1009",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003344",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003344",
abstract = "We define two asymptotically optimal towers over
quadratic fields, and give the explicit descriptions of
the ramification loci and the sets of places splitting
completely, which relate to the elliptic modular curves
X$_0$ (4$^n$) and X$_0$ (3$^n$ ), respectively.
Moreover, in the last section, we determine completely
the modularity of a tower given by Maharaj and
Wulftange in [18].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ih:2010:FPP,
author = "Su-Ion Ih and Thomas J. Tucker",
title = "A Finiteness Property for Preperiodic Points of
{Chebyshev} Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1011--1025",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003356",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003356",
abstract = "Let K be a number field with algebraic closure, let S
be a finite set of places of K containing the
Archimedean places, and let \phi be a Chebyshev
polynomial. We prove that if is not preperiodic, then
there are only finitely many preperiodic points which
are S-integral with respect to \alpha.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gottesman:2010:QRP,
author = "Richard Gottesman and Kwokfung Tang",
title = "Quadratic Recurrences with a Positive Density of Prime
Divisors",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1027--1045",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003368",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003368",
abstract = "For f(x) \in {\mathbb{Z}}[x] and a \in {\mathbb{Z}},
we let f$^n$ (x) be the nth iterate of f(x), P(f, a) =
{p prime: p|f$^n$ (a) for some n}, and D(P(f, a))
denote the natural density of P(f, a) within the set of
primes. A conjecture of Jones [5] indicates that D(P(f,
a)) = 0 for most quadratic f. In this paper, we find an
exceptional family of (f, a) such that D(P(f, a)) > 0
by considering f$_t$ (x) = (x + t)$^2$- 2 - t and a$_t$
= f$_t$ (0) for t \in {\mathbb{Z}}. We prove that if t
is not of the form \pm M$^2$ \pm 2 or \pm 2M$^2$ \pm 2,
then D(P(f$_t$, a$_t$)) = {\u{2}153}. We also determine
D(P(f$_t$, a$_t$)) in some cases when the density is
not equal to {\u{2}153}. Our results suggest a
connection between the arithmetic dynamics of the
conjugates of x$^2$ and the conjugates of x$^2$- 2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hoshi:2010:FIP,
author = "Akinari Hoshi and Katsuya Miyake",
title = "On the Field Intersection Problem of Solvable Quintic
Generic Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1047--1081",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000337X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000337X",
abstract = "We study a general method of the field intersection
problem of generic polynomials over an arbitrary field
k via formal Tschirnhausen transformation. In the case
of solvable quintic, we give an explicit answer to the
problem by using multi-resolvent polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knopp:2010:ECG,
author = "Marvin Knopp and Wissam Raji",
title = "{Eichler} Cohomology for Generalized Modular Forms
{II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1083--1090",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000340X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000340X",
abstract = "We derive further results on Eichler cohomology of
generalized modular forms of arbitrary real weight.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Agashe:2010:SSV,
author = "Amod Agashe",
title = "Squareness in the Special {$L$}-Value and Special
{$L$}-Values of Twists",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1091--1111",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003393",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003393",
abstract = "Let N be a prime and let A be a quotient of J$_0$ (N)
over Q associated to a newform such that the special
$L$-value of A (at s = 1) is non-zero. Suppose that the
algebraic part of the special $L$-value of A is
divisible by an odd prime q such that q does not divide
the numerator of. Then the Birch and Swinnerton-Dyer
conjecture predicts that the $q$-adic valuations of the
algebraic part of the special $L$-value of A and of the
order of the Shafarevich--Tate group are both positive
even numbers. Under a certain mod q non-vanishing
hypothesis on special $L$-values of twists of A, we
show that the $q$-adic valuations of the algebraic part
of the special $L$-value of A and of the Birch and
Swinnerton-Dyer conjectural order of the
Shafarevich--Tate group of A are both positive even
numbers. We also give a formula for the algebraic part
of the special $L$-value of A over quadratic imaginary
fields K in terms of the free abelian group on
isomorphism classes of supersingular elliptic curves in
characteristic N (equivalently, over conjugacy classes
of maximal orders in the definite quaternion algebra
over Q ramified at N and \infty) which shows that this
algebraic part is a perfect square up to powers of the
prime two and of primes dividing the discriminant of K.
Finally, for an optimal elliptic curve of arbitrary
conductor E, we give a formula for the special
$L$-value of the twist E$_{-D}$ of E by a negative
fundamental discriminant -D, which shows that this
special $L$-value is an integer up to a power of 2,
under some hypotheses. In view of the second part of
the Birch and Swinnerton-Dyer conjecture, this leads us
to the surprising conjecture that the square of the
order of the torsion subgroup of E$_{-D}$ divides the
product of the order of the Shafarevich--Tate group of
E$_{-D}$ and the orders of the arithmetic component
groups of E$_{-D}$, under certain mild hypotheses.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Matomaki:2010:NSN,
author = "Kaisa Matom{\"a}ki",
title = "A Note on Smooth Numbers in Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1113--1116",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003381",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003381",
abstract = "We prove that, for any \in > 0, there exists a
constant C > 0 such that the interval contains numbers
whose all prime factors are smaller than.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Shemanske:2010:CSH,
author = "T. Shemanske and S. Treneer and L. Walling",
title = "Constructing Simultaneous {Hecke} Eigenforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1117--1137",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003411",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003411",
abstract = "It is well known that newforms of integral weight are
simultaneous eigenforms for all the Hecke operators,
and that the converse is not true. In this paper, we
give a characterization of all simultaneous Hecke
eigenforms associated to a given newform, and provide
several applications. These include determining the
number of linearly independent simultaneous eigenforms
in a fixed space which correspond to a given newform,
and characterizing several situations in which the full
space of cusp forms is spanned by a basis consisting of
such eigenforms. Part of our results can be seen as a
generalization of results of Choie--Kohnen who
considered diagonalization of ``bad'' Hecke operators
on spaces with square-free level and trivial character.
Of independent interest, but used herein, is a lower
bound for the dimension of the space of newforms with
arbitrary character.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kleinbock:2010:MDA,
author = "Dmitry Kleinbock and Gregory Margulis and Junbo Wang",
title = "Metric {Diophantine} Approximation for Systems of
Linear Forms Via Dynamics",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1139--1168",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003423",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003423",
abstract = "The goal of this paper is to generalize the main
results of [21] and subsequent papers on metric with
dependent quantities to the set-up of systems of linear
forms. In particular, we establish ``joint strong
extremality'' of arbitrary finite collection of smooth
non-degenerate submanifolds of {\mathbb{R}}$^n$. The
proofs are based on generalized quantitative
non-divergence estimates for translates of measures on
the space of lattices.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hoelscher:2010:RCG,
author = "Jing Long Hoelscher",
title = "Ray Class Groups of Quadratic and Cyclotomic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1169--1182",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003447",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003447",
abstract = "This paper studies Galois extensions over real
quadratic number fields or cyclotomic number fields
ramified only at one prime. In both cases, the ray
class groups are computed, and they give restrictions
on the finite groups that can occur as such Galois
groups. Let be a real quadratic number field with a
prime P lying above p in {$ \mathbb {Q} $}. If p splits
in K/{$ \mathbb {Q} $} and p does not divide the big
class number of K, then any pro-p extension of K
ramified only at P is finite cyclic. If p is inert in
K/{$ \mathbb {Q} $}, then there exist infinite
extensions of K ramified only at P. Furthermore, for
big enough integer k, the ray class field (mod P$^{k +
1}$) is obtained from the ray class field (mod P$^k$)
by adjoining $ \zeta_{p^{k + 1}}$. In the case of a
regular cyclotomic number field $ K = \mathbb
{Q}(\zeta_p)$, the explicit structure of ray class
groups $ (m o d P^k)$ is given for any positive integer
$k$, where $P$ is the unique prime in $K$ above $p$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ulas:2010:VHT,
author = "Maciej Ulas",
title = "Variations on Higher Twists of Pairs of Elliptic
Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1183--1189",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003472",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003472",
abstract = "In this note we show that for any pair of elliptic
curves E$_1$, E$_2$ over {$ \mathbb {Q}$} with
j-invariant equal to 0, we can find a polynomial D \in
{\mathbb{Z}}[u, v, w, t] such that the sextic twists of
the curves E$_1$, E$_2$ by D(u, v, w, t) have rank \geq
2 over the field {$ \mathbb {Q}$}(u, v, w, t). A
similar result is proved for simultaneous quartic
twists of pairs of elliptic curves with j-invariant
1728.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Villa-Salvador:2010:EPC,
author = "Gabriel Villa-Salvador",
title = "An Elementary Proof of the Conductor--Discriminant
Formula",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "5",
pages = "1191--1197",
month = aug,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003459",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003459",
abstract = "For a finite abelian extension K/{$ \mathbb {Q} $},
the conductor-discriminant formula establishes that the
absolute value of the discriminant of K is equal to the
product of the conductors of the elements of the group
of Dirichlet characters associated to K. The simplest
proof uses the functional equation for the Dedekind
zeta function of K and its expression as the product of
the $L$-series attached to the various Dirichlet
characters associated to K. In this paper, we present
an elementary proof of this formula considering first K
contained in a cyclotomic number field of p$^n$-roots
of unity, where p is a prime number, and in the general
case, using the ramification index of p given by the
group of Dirichlet characters.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baczkowski:2010:V,
author = "Daniel Baczkowski and Michael Filaseta and Florian
Luca and Ognian Trifonov",
title = "On values of $ d(n!) / m! $, $ \varphi (n!) / m! $ and
$ \sigma (n!) / m! $",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1199--1214",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110003435",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003435",
abstract = "For f one of the classical arithmetic functions d,
\varphi and \sigma, we establish constraints on the
quadruples (n, m, a, b) of integers satisfying f(n!)/m!
= a/b. In particular, our results imply that as nm
tends to infinity, the number of distinct prime
divisors dividing the product of the numerator and
denominator of the fraction f(n!)/m!, when reduced,
tends to infinity.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kable:2010:AIO,
author = "Anthony C. Kable",
title = "An Arithmetical Invariant of Orbits of Affine Actions
and Its Application to Similarity Classes of Quadratic
Spaces",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1215--1253",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003460",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003460",
abstract = "Given an action of an affine algebraic group on an
affine variety and a relatively invariant regular
function, all defined over the ring of integers of a
number field and having suitable additional properties,
an invariant of the rational orbits of the action is
defined. This invariant, the reduced replete Steinitz
class, takes its values in the reduced replete class
group of the number field. The general framework is
then applied to obtain an invariant of similarity
classes of non-degenerate quadratic spaces of even
rank. The invariant is related to more familiar
invariants. It is shown that if the similarity classes
are weighted by the volume of an associated
automorphism group then their reduced replete Steinitz
classes are asymptotically uniformly distributed with
respect to a natural parameter.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kohnen:2010:SNF,
author = "Winfried Kohnen",
title = "A Short Note on {Fourier} Coefficients of
Half-Integral Weight Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1255--1259",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003484",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003484",
abstract = "We give an unconditional proof of a result on sign
changes of Fourier coefficients of cusp forms of
half-integral weight that before was proved only under
the hypothesis of Chowla's conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vaserstein:2010:PPP,
author = "Leonid Vaserstein and Takis Sakkalis and Sophie
Frisch",
title = "Polynomial Parametrization of {Pythagorean} Tuples",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1261--1272",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003496",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003496",
abstract = "A Pythagorean (k, l)-tuple over a commutative ring A
is a vector x = (x$_i$) \in A$^{k + l}$, where k, l \in
\mathbb{N}, k \geq l which satisfies. In this paper, a
polynomial parametrization of Pythagorean (k, l)-tuples
over the ring F[t] is given, for l \geq 2. In the case
where l = 1, solutions of the above equation are
provided for k = 2, 3, 4, 5, and 9.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mammo:2010:DDA,
author = "Behailu Mammo",
title = "On the Density of Discriminants of {Abelian}
Extensions of a Number Field",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1273--1291",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003502",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003502",
abstract = "Let G = C$_{\ell }$ $ \times $ C$_{\ell }$ denote the
product of two cyclic groups of prime order \ell, and
let k be an algebraic number field. Let N(k, G, m)
denote the number of abelian extensions K of k with
Galois group G(K/k) isomorphic to G, and the relative
discriminant {$ \mathcal {D} $}(K/k) of norm equal to
m. In this paper, we derive an asymptotic formula for $
\sum_{m \leq X}$ N(k, G; m). This extends the result
previously obtained by Datskovsky and Mammo.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lozano-Robledo:2010:BTE,
author = "{\'A}lvaro Lozano-Robledo and Benjamin Lundell",
title = "Bounds for the Torsion of Elliptic Curves Over
Extensions with Bounded Ramification",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1293--1309",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003514",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003514",
abstract = "Let E be a semi-stable elliptic curve defined over {$
\mathbb {Q} $}, and fix N \geq 2. Let $ K_N $ /{$
\mathbb {Q} $} be a maximal algebraic Galois extension
of {$ \mathbb {Q} $} whose ramification indices are all
at most N. We show that there exists a computable bound
B(N), which depends only on N and not on the choice of
E/{$ \mathbb {Q} $}, such that the size of
E(K$_N$)$_{Tors}$ is always at most B(N).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jahangiri:2010:GAQ,
author = "Majid Jahangiri",
title = "Generators of Arithmetic Quaternion Groups and a
{Diophantine} Problem",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1311--1328",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003551",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003551",
abstract = "Let p be a prime and a a quadratic non-residue (mod
p). Then the set of integral solutions of the
Diophantine equation form a cocompact discrete subgroup
\Gamma$_{p, a}$ \subset SL(2, {\mathbb{R}}) which is
commensurable with the group of units of an order in a
quaternion algebra over {$ \mathbb {Q}$}. The problem
addressed in this paper is an estimate for the traces
of a set of generators for \Gamma$_{p, a}$. Empirical
results summarized in several tables show that the
trace has significant and irregular fluctuations which
is reminiscent of the behavior of the size of a
generator for the solutions of Pell's equation. The
geometry and arithmetic of the group of units of an
order in a quaternion algebra play a key role in the
development of the code for the purpose of this
paper.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tanti:2010:ECS,
author = "Jagmohan Tanti and S. A. Katre",
title = "{Euler}'s Criterion for Septic Nonresidues",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1329--1347",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003563",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003563",
abstract = "Let p be a prime \equiv 1 (mod 7). In this paper, we
obtain an explicit expression for a primitive seventh
root of unity (mod p) in terms of coefficients of a
Jacobi sum of order 7 and also in terms of a solution
of a Diophantine system of Leonard and Williams, and
then obtain Euler's criterion for septic nonresidues D
(mod p) in terms of this seventh root. Explicit results
are given for septic nonresidues for D = 2, 3, 5, 7.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Booher:2010:ECT,
author = "Jeremy Booher and Anastassia Etropolski and Amanda
Hittson",
title = "Evaluations of Cubic Twisted {Kloosterman} Sheaf
Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1349--1365",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003538",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003538",
abstract = "We prove some conjectures of Evans and Katz presented
in a paper by Evans regarding twisted Kloosterman sheaf
sums T$_n$. These conjectures give explicit evaluations
of the sums T$_n$ where the character is cubic and n =
4. There are also conjectured relationships between
evaluations of T$_n$ and the coefficients of certain
modular forms. For three of these modular forms, each
of weight 3, it is conjectured that the coefficients
are related to the squares of the coefficients of
weight 2 modular forms. We prove these relationships
using the theory of complex multiplication.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Verrill:2010:CRM,
author = "H. A. Verrill",
title = "Congruences Related to Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1367--1390",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003587",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003587",
abstract = "Let $f$ be a modular form of weight $k$ for a
congruence subgroup $ \Gamma \subset \mathrm {SL}_2
(Z)$, and $t$ a weight $0$ modular function for $
\Gamma $. Assume that near $ t = 0$, we can write $ f =
\sum_{n \geq 0} b_n t^n$, $ b_n \in Z$. Let $ \ell (z)$
be a weight $ k + 2$ modular form with $q$-expansion $
\sum \gamma_n q^n$, such that the Mellin transform of $
\ell $ can be expressed as an Euler product. Then we
show that if for some integers $ a_i$, $ d_i$, then the
congruence relation $ b_{mp^r} - \gamma_p b_{mp^{r -
1}} + \varepsilon_p p^{k + 1} b_{mp^{r - 2}} \equiv 0
(\bmod p^r)$ holds. We give a number of examples of
this phenomena.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{David:2010:SFD,
author = "Chantal David and Jorge Jim{\'e}nez Urroz",
title = "Square-Free Discriminants of {Frobenius} Rings",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1391--1412",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003599",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003599",
abstract = "Let E be an elliptic curve over {$ \mathbb {Q} $}. We
know that the ring of endomorphisms of its reduction
modulo an ordinary prime p is an order of the quadratic
imaginary field generated by the Frobenius element
\pi$_p$. However, except in the trivial case of complex
multiplication, very little is known about the fields
that appear as algebras of endomorphisms when p varies.
In this paper, we study the endomorphism ring by
looking at the arithmetic of, the discriminant of the
characteristic polynomial of \pi$_p$. In particular, we
give a precise asymptotic for the function counting the
number of primes p up to x such that is square-free and
in certain congruence class fixed {\em a priori\/},
when averaging over elliptic curves defined over the
rationals. We discuss the relation of this result with
the Lang--Trotter conjecture, and some other questions
on the curve modulo p.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hambleton:2010:QRR,
author = "S. Hambleton and V. Scharaschkin",
title = "Quadratic Reciprocity Via Resultants",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1413--1417",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000354X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000354X",
abstract = "We give a simple inductive proof of quadratic
reciprocity using resultants.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lebacque:2010:TVI,
author = "Philippe Lebacque",
title = "On {Tsfasman--Vl{\u{a}}du{\c{t}}} invariants of
infinite global fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "6",
pages = "1419--1448",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003526",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003526",
abstract = "In this paper, we study certain asymptotic properties
of global fields. We consider the set of
Tsfasman--Vl{\u{a}}du{\c{t}} invariants of infinite
global fields and answer some natural questions arising
from their work. In particular, we prove the existence
of infinite global fields having finitely many strictly
positive invariants at given places, and the existence
of infinite number fields with certain prescribed
invariants being zero. We also give precisions on the
deficiency of infinite global fields and on the primes
decomposition in those fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dujella:2010:SSP,
author = "Andrej Dujella and Ana Jurasi{\'c}",
title = "On the Size of Sets in a Polynomial Variant of a
Problem of {Diophantus}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1449--1471",
month = nov,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110003575",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003575",
abstract = "In this paper, we prove that there does not exist a
set of 8 polynomials (not all constant) with
coefficients in an algebraically closed field of
characteristic 0 with the property that the product of
any two of its distinct elements plus 1 is a perfect
square.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ehlen:2010:TBP,
author = "Stephan Ehlen",
title = "Twisted {Borcherds} Products on {Hilbert} Modular
Surfaces and the Regularized Theta Lift",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1473--1489",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003642",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003642",
abstract = "We construct a lifting from weakly holomorphic modular
forms of weight 0 for SL$_2$ ({\mathbb{Z}}) with
integral Fourier coefficients to meromorphic Hilbert
modular forms of weight 0 for the full Hilbert modular
group of a real quadratic number field with an infinite
product expansion and a divisor given by a linear
combination of twisted Hirzebruch--Zagier divisors. The
construction uses the singular theta lifting by
considering a suitable twist of a Siegel theta
function. We generalize the work by Bruinier and Yang
who showed the existence of the lifting for prime
discriminants using a different approach.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Belabas:2010:DCP,
author = "Karim Belabas and {\'E}tienne Fouvry",
title = "Discriminants cubiques et progressions
arithm{\'e}tiques. ({French}) [{Cubic} discriminants
and arithmetic progressions]",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1491--1529",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003605",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003605",
abstract = "Nous calculons la densit{\'e} des discriminants des
corps sextiques galoisiens de groupe S$_3$,
d{\'e}montrant un nouveau cas de la conjecture de Malle
ainsi qu'un cas particulier de sa
g{\'e}n{\'e}ralisation par Ellenberg et Venkatesh. Plus
g{\'e}n{\'e}ralement, nous {\'e}tudions la densit{\'e}
des discriminants de corps cubiques dans une
progression arithm{\'e}tique, avec une zone
d'uniformit{\'e} la plus large possible. We compute the
density of discriminants of Galois sextic fields with
group S$_3$, thereby proving a new case of Malle's
conjecture as well as a special case of its
generalization by Ellenberg and Venkatesh. Further, we
study the density of cubic discriminants in an
arithmetic progression, in the largest possible
uniformity with respect to the modulus.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Patkowski:2010:CGF,
author = "Alexander E. Patkowski",
title = "On Curious Generating Functions for Values of
{$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1531--1540",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003630",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003630",
abstract = "We prove some curious identities for generating
functions for values of {$L$}-functions. It is shown
how to obtain generating functions for values of
{$L$}-functions using a slightly different approach,
resulting in some new $q$-series identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wu:2010:RGD,
author = "Qingquan Wu and Renate Scheidler",
title = "The Ramification Groups and Different of a Compositum
of {Artin--Schreier} Extensions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1541--1564",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003617",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003617",
abstract = "Let K be a function field over a perfect constant
field of positive characteristic p, and L the
compositum of n (degree p) Artin--Schreier extensions
of K. Then much of the behavior of the degree p$^n$
extension L/K is determined by the behavior of the
degree p intermediate extensions M/K. For example, we
prove that a place of K totally ramifies/is
inert/splits completely in L if and only if it totally
ramifies/is inert/splits completely in every M.
Examples are provided to show that all possible
decompositions are in fact possible; in particular, a
place can be inert in a non-cyclic Galois function
field extension, which is impossible in the case of a
number field. Moreover, we give an explicit closed form
description of all the different exponents in L/K in
terms of those in all the M/K. Results of a similar
nature are given for the genus, the regulator, the
ideal class number and the divisor class number. In
addition, for the case n = 2, we provide an explicit
description of the ramification group filtration of
L/K.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pickett:2010:CSD,
author = "Erik Jarl Pickett",
title = "Construction of Self-Dual Integral Normal Bases in
{Abelian} Extensions of Finite and Local Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1565--1588",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003654",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003654",
abstract = "Let F/E be a finite Galois extension of fields with
abelian Galois group \Gamma. A self-dual normal basis
for F/E is a normal basis with the additional property
that Tr$_{F / E}$ (g(x), h(x)) = \delta$_{g, h}$ for g,
h \in \Gamma. Bayer-Fluckiger and Lenstra have shown
that when char(E) \neq 2, then F admits a self-dual
normal basis if and only if [F : E] is odd. If F/E is
an extension of finite fields and char(E) = 2, then F
admits a self-dual normal basis if and only if the
exponent of \Gamma is not divisible by 4. In this
paper, we construct self-dual normal basis generators
for finite extensions of finite fields whenever they
exist. Now let K be a finite extension of {$ \mathbb
{Q}$}$_p$, let L/K be a finite abelian Galois extension
of odd degree and let be the valuation ring of L. We
define A$_{L / K}$ to be the unique fractional -ideal
with square equal to the inverse different of L/K. It
is known that a self-dual integral normal basis exists
for A$_{L / K}$ if and only if L/K is weakly ramified.
Assuming p \neq 2, we construct such bases whenever
they exist.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Robertson:2010:MCF,
author = "Leanne Robertson",
title = "Monogeneity in Cyclotomic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1589--1607",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003666",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003666",
abstract = "A number field is said to be {\em monogenic\/} if its
ring of integers is a simple ring extension
{\mathbb{Z}}[\alpha ] of {\mathbb{Z}}. It is a
classical and usually difficult problem to determine
whether a given number field is monogenic and, if it
is, to find all numbers \alpha that generate a power
integral basis {1, \alpha, \alpha$^2$, \ldots,
\alpha$^k$ } for the ring. The nth cyclotomic field {$
\mathbb {Q}$}(\zeta$_n$) is known to be monogenic for
all n, and recently Ranieri proved that if n is coprime
to 6, then up to integer translation all the integral
generators for {$ \mathbb {Q}$}(\zeta$_n$) lie on the
unit circle or the line Re(z) = 1/2 in the complex
plane. We prove that this geometric restriction extends
to the cases n = 3k and n = 4k, where k is coprime to
6. We use this result to find all power integral bases
for {$ \mathbb {Q}$}(\zeta$_n$) for n = 15, 20, 21, 28.
This leads us to a conjectural solution to the problem
of finding all integral generators for cyclotomic
fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Feigon:2010:EAC,
author = "Brooke Feigon and David Whitehouse",
title = "Exact Averages of Central Values of Triple Product
{$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1609--1624",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000368X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000368X",
abstract = "We obtain exact formulas for central values of triple
product {$L$}-functions averaged over newforms of
weight 2 and prime level. We apply these formulas to
non-vanishing problems. This paper uses a period
formula for the triple product {$L$}-function proved by
Gross and Kudla.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Katayama:2010:GGF,
author = "Koji Katayama",
title = "Generalized Gamma Functions with Characters",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1625--1657",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003629",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003629",
abstract = "The main objective of this paper is to define \Gamma
functions \Gamma [\chi ](v) with characters \chi and
study their properties. To this end, we ought to
introduce {$L$}-functions of Hurwitz type. We prove
that holds, which combines the theory at ``s = 0'' and
the theory at ``s = 1''.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bostan:2010:GFC,
author = "Alin Bostan and Bruno Salvy and Khang Tran",
title = "Generating Functions of {Chebyshev}-Like Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1659--1667",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003691",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003691",
abstract = "In this short note, we give simple proofs of several
results and conjectures formulated by Stolarsky and
Tran concerning generating functions of some families
of Chebyshev-like polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lee:2010:SPF,
author = "K. S. Enoch Lee",
title = "On the Sum of a Prime and a {Fibonacci} Number",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1669--1676",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003708",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003708",
abstract = "We show that the set of the numbers that are the sum
of a prime and a Fibonacci number has positive lower
asymptotic density.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dewar:2010:RCS,
author = "Michael Dewar and Olav K. Richter",
title = "{Ramanujan} Congruences for {Siegel} Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1677--1687",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000371X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000371X",
abstract = "We determine conditions for the existence and
non-existence of Ramanujan-type congruences for Jacobi
forms. We extend these results to Siegel modular forms
of degree 2 and as an application, we establish
Ramanujan-type congruences for explicit examples of
Siegel modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Schwab:2010:GAF,
author = "Emil Daniel Schwab",
title = "Generalized Arithmetical Functions of Three
Variables",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1689--1699",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003721",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003721",
abstract = "The paper is devoted to the study of some properties
of generalized arithmetical functions extended to the
case of three variables. The convolution in this case
is a convolution of the incidence algebra of a
M{\"o}bius category in the sense of Leroux. This
category is a two-sided analogue of the poset (it is
viewed as a category) of positive integers ordered by
divisibility.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sairaiji:2010:FGJ,
author = "Fumio Sairaiji",
title = "Formal Groups of {Jacobian} Varieties of Hyperelliptic
Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "7",
pages = "1701--1716",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003733",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:23 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003733",
abstract = "Let k be a field of characteristic zero. In this
paper, we discuss two explicit constructions of the
formal groups {\u{0}134} of the Jacobian varieties J of
hyperelliptic curves C over k. Our results are
generalizations of the classical constructions of
formal groups of elliptic curves. As an application of
our results, we may decide the type of bad reduction of
J modulo p when C is a hyperelliptic curve over {$
\mathbb {Q} $}.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Templier:2010:AVC,
author = "Nicolas Templier",
title = "On Asymptotic Values of Canonical Quadratic
{$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1717--1730",
month = dec,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042110003678",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003678",
abstract = "We establish an asymptotic for the first moment of
Hecke $L$-series associated to canonical characters on
imaginary quadratic fields. This provides another proof
and improves recent results by Masri and
Kim--Masri--Yang.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Samuels:2010:FCU,
author = "Charles L. Samuels",
title = "The Finiteness of Computing the Ultrametric {Mahler}
Measure",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1731--1753",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003745",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003745",
abstract = "Recent work of Fili and the author examines an
ultrametric version of the Mahler measure, denoted
M$_{\infty }$ (\alpha) for an algebraic number \alpha.
We show that the computation of M$_{\infty }$ (\alpha)
can be reduced to a certain search through a finite
set. Although it is an open problem to record the
points of this set in general, we provide some examples
where it is reasonable to compute and our result can be
used to determine M$_{\infty }$ (\alpha).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kang:2010:APT,
author = "Soon-Yi Kang and Chang Heon Kim",
title = "Arithmetic Properties of Traces of Singular Moduli on
Congruence Subgroups",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1755--1768",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003757",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003757",
abstract = "After Zagier proved that the traces of singular moduli
are Fourier coefficients of a weakly holomorphic
modular form, various arithmetic properties of the
traces of singular values of modular functions mostly
on the full modular group have been found. The purpose
of this paper is to generalize the results for modular
functions on congruence subgroups with arbitrary
level.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sbeity:2010:CSE,
author = "Farah Sbeity and Boucha{\"i}b Soda{\"i}gui",
title = "Classes de {Steinitz} d'extensions non ab{\'e}liennes
{\`a} groupe de {Galois} d'ordre $1$6 ou
extrasp{\'e}cial d'ordre $ 32$ et probl{\`e}me de
plongement. ({French}) [{Steinitz} classes of
non-Abelian extensions to {Galois} group of order $ 16
$ or extraspecial of order $ 32$ and embedding
problem]",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1769--1783",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003794",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003794",
abstract = "Soient k un corps de nombres et Cl(k) son groupe des
classes. Soit \Gamma un groupe non ab{\'e}lien d'ordre
16, ou un groupe extrasp{\'e}cial d'ordre 32. Soit
R$_m$ (k, \Gamma) le sous-ensemble de Cl(k) form{\'e}
par les {\'e}l{\'e}ments qui sont r{\'e}alisables par
les classes de Steinitz d'extensions galoisiennes de k,
mod{\'e}r{\'e}ment ramifi{\'e}es et dont le groupe de
Galois est isomorphe {\`a} \Gamma. Lorsque \Gamma est
le groupe modulaire d'ordre 16, on suppose que k
contienne une racine primitive 4{\`e}me de l'unit{\'e}.
Dans cet article on montre que R$_m$ (k, \Gamma) est le
groupe Cl(k) tout entier si le nombre des classes de k
est impair. On {\'e}tudie un probl{\`e}me de plongement
en liaison avec les classes de Steinitz dans la
perspective de l'{\'e}tude des classes galoisiennes
r{\'e}alisables. On prouve que pour tout c \in Cl(k),
il existe une extension quadratique de k,
mod{\'e}r{\'e}e, dont la classe de Steinitz est c, et
qui est plongeable dans une extension galoisienne de k,
mod{\'e}r{\'e}e et {\`a} groupe de Galois isomorphe
{\`a} \Gamma. Let k be a number field and Cl(k) its
class group. Let \Gamma be a nonabelian group of order
16 or an extra-special group of order 32. Let R$_m$ (k,
\Gamma) be the subset of Cl(k) consisting of those
classes which are realizable as Steinitz classes of
tame Galois extensions of k with Galois group
isomorphic to \Gamma. When \Gamma is the modular group
of order 16, we assume that k contains a primitive 4th
root of unity. In the present paper, we show that R$_m$
(k, \Gamma) is the full group Cl(k) if the class number
of k is odd. We study an embedding problem connected
with Steinitz classes in the perspective of studying
realizable Galois module classes. We prove that for all
c \in Cl(k), there exist a tame quadratic extension of
k, with Steinitz class c, and which is embeddable in a
tame Galois extension of k with Galois group isomorphic
to \Gamma.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Lucht:2010:SRE,
author = "Lutz G. Lucht",
title = "A Survey of {Ramanujan} Expansions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1785--1799",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003800",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003800",
abstract = "This paper summarizes the development of Ramanujan
expansions of arithmetic functions since Ramanujan's
paper in 1918, following Carmichael's mean-value-based
concept from 1932 up to 1994. A new technique, based on
the concept of related arithmetic functions, is
introduced that leads to considerable extensions of
preceding results on Ramanujan expansions. In
particular, very short proofs of theorems for additive
and multiplicative functions going far beyond previous
borders are presented, and Ramanujan expansions that
formerly have been considered mysterious are
explained.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cai:2010:LFS,
author = "Yingchun Cai",
title = "{Lagrange}'s Four Squares Theorem with Variables of
Special Type",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1801--1817",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003812",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003812",
abstract = "Let N denote a sufficiently large integer satisfying N
\equiv 4 (mod 24), and P$_r$ denote an almost-prime
with at most r prime factors, counted according to
multiplicity. In this paper, we proved that the
equation is solvable in one prime and three P$_{42}$,
or in four P$_{13}$. These results constitute
improvements upon that of Heath-Brown and Tolev.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Barman:2010:IIT,
author = "Rupam Barman and Anupam Saikia",
title = "{Iwasawa} $ \lambda $-invariants and {$ \Gamma
$}-transforms of $p$-adic measures on {$ \mathbb
{Z}_p^n $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1819--1829",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003824",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003824",
abstract = "In this paper, we determine a relation between the
\lambda -invariants of a $p$-adic measure on and its
\Gamma transform. Along the way we also determine
$p$-adic properties of certain Mahler coefficients.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Caranay:2010:ESP,
author = "Perlas C. Caranay and Renate Scheidler",
title = "An Efficient Seventh Power Residue Symbol Algorithm",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1831--1853",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003770",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003770",
abstract = "Power residue symbols and their reciprocity laws have
applications not only in number theory, but also in
other fields like cryptography. A crucial ingredient in
certain public key cryptosystems is a fast algorithm
for computing power residue symbols. Such algorithms
have only been devised for the Jacobi symbol as well as
for cubic and quintic power residue symbols, but for no
higher powers. In this paper, we provide an efficient
procedure for computing 7th power residue symbols. The
method employs arithmetic in the field {$ \mathbb {Q}
$}(\zeta), with \zeta a primitive 7th root of unity,
and its ring of integers {\mathbb{Z}}[\zeta ]. We give
an explicit characterization for an element in
{\mathbb{Z}}[\zeta ] to be primary, and provide an
algorithm for finding primary associates of integers in
{\mathbb{Z}}[\zeta ]. Moreover, we formulate explicit
forms of the complementary laws to Kummer's 7th degree
reciprocity law, and use Lenstra's norm-Euclidean
algorithm in the cyclotomic field.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{DelCorso:2010:NII,
author = "Ilaria {Del Corso} and Roberto Dvornicich",
title = "Non-Invariance of the Index in Wildly Ramified
Extensions",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1855--1868",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003836",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003836",
abstract = "In this paper, we give an example of three wildly
ramified extensions L$_1$, L$_2$, L$_3$ of {$ \mathbb
{Q}$}$_2$ with the same ramification numbers and
isomorphic Galois groups, such that I(nL$_1$ ) >
I(nL$_2$) > I(nL$_3$) for a suitable integer n (where
I(nL) denotes the index of the {$ \mathbb
{Q}$}$_2$-algebra L$^n$). This example shows that the
condition given in [2] for the invariance of the index
of tamely ramified extensions is no longer sufficient
in the general case.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Laishram:2010:CRP,
author = "Shanta Laishram",
title = "On a Conjecture on {Ramanujan} Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1869--1873",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003848",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003848",
abstract = "For n \geq 1, the {\em nth Ramanujan prime\/} is
defined to be the smallest positive integer R$_n$ with
the property that if x \geq R$_n$, then where \pi (\nu)
is the number of primes not exceeding \nu for any \nu >
0 and \nu \in {\mathbb{R}}. In this paper, we prove a
conjecture of Sondow on upper bound for Ramanujan
primes. An explicit bound of Ramanujan primes is also
given. The proof uses explicit bounds of prime \pi and
\theta functions due to Dusart.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vienney:2010:NCA,
author = "Mathieu Vienney",
title = "A new construction of $p$-adic {Rankin} convolutions
in the case of positive slope",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1875--1900",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003782",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003782",
abstract = "Given two newforms f and g of respective weights k and
l with l < k, Hida constructed a $p$-adic
{$L$}-function interpolating the values of the Rankin
convolution of f and g in the critical strip l \leq s
\leq k. However, this construction works only if f is
an ordinary form. Using a method developed by
Panchishkin to construct $p$-adic {$L$}-function
associated with modular forms, we generalize this
construction to the case where the slope of f is
small.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Brown:2010:SVF,
author = "Jim Brown",
title = "Special values of {$L$}-functions on {$ \mathrm
{GSp}_4 \times \mathrm {GL}_2$} and the non-vanishing
of {Selmer} groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1901--1926",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003769",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003769",
abstract = "In this paper, we show how one can use an inner
product formula of Heim giving the inner product of the
pullback of an Eisenstein series from Sp$_{10}$ to
Sp$_2$ $ \times $ Sp$_4$ $ \times $ Sp$_4$ with a
new-form on GL$_2$ and a Saito--Kurokawa lift to
produce congruences between Saito--Kurokawa lifts and
non-CAP forms. This congruence is in part controlled by
the {$L$}-function on GSp$_4$ $ \times $ GL$_2$. The
congruence is then used to produce nontrivial torsion
elements in an appropriate Selmer group, providing
evidence for the Bloch--Kato conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kaneko:2010:KDM,
author = "Masanobu Kaneko and Yasuo Ohno",
title = "On a Kind of Duality of Multiple Zeta-Star Values",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1927--1932",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S179304211000385X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211000385X",
abstract = "A duality-type relation for height one multiple
zeta-star values is established. A conjectural
generalization to the case of arbitrary height is also
presented.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bettin:2010:SMR,
author = "Sandro Bettin",
title = "The Second Moment of the {Riemann} Zeta Function with
Unbounded Shifts",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1933--1944",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003861",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003861",
abstract = "We prove an asymptotic formula for the second moment
(up to height T) of the Riemann zeta function with two
shifts. The case we deal with is where the real parts
of the shifts are very close to zero and the imaginary
parts can grow up to T$^{2 - \varepsilon }$, for any
\varepsilon > 0.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2010:AIV,
author = "Anonymous",
title = "Author Index (Volume 6)",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "8",
pages = "1945--1950",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003885",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042110003885",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Joshi:2011:IHC,
author = "Kirti Joshi and Cameron Mcleman",
title = "Infinite {Hilbert} Class Field Towers from {Galois}
Representations",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "1--8",
month = feb,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111003879",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003879",
abstract = "We investigate class field towers of number fields
obtained as fixed fields of modular representations of
the absolute Galois group of the rational numbers.
First, for each k \in {12, 16, 18, 20, 22, 26}, we give
explicit rational primes \ell such that the fixed field
of the mod-\ell representation attached to the unique
normalized cusp eigenform of weight k on SL$_2$
({\mathbb{Z}}) has an infinite class field tower.
Further, under a conjecture of Hardy and Littlewood, we
prove the existence of infinitely many cyclotomic
fields of prime conductor, providing infinitely many
such primes \ell for each k in the list. Finally, given
a non-CM curve E/{$ \mathbb {Q}$}, we show that there
exists an integer M$_E$ such that the fixed field of
the representation attached to the n-division points of
E has an infinite class field tower for a set of
integers n of density one among integers coprime to
M$_E$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nguyen:2011:CDM,
author = "Lan Nguyen",
title = "A Complete Description of Maximal Solutions of
Functional Equations Arising from Multiplication of
Quantum Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "9--56",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003909",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003909",
abstract = "In this paper, we resolve a problem raised by
Nathanson concerning the maximal solutions to
functional equations naturally arising from
multiplication of quantum integers ([4]). Together with
our results obtained in [11], which treats the case
where the field of coefficients is {$ \mathbb {Q} $},
this provides a complete description of the maximal
solutions to these functional equations and their
support bases P in characteristic zero setting.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Heuberger:2011:PDA,
author = "Clemens Heuberger and Helmut Prodinger",
title = "A precise description of the $p$-adic valuation of the
number of alternating sign matrices",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "57--69",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003892",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003892",
abstract = "Following Sun and Moll ([4]), we study v$_p$ (T(N)),
the $p$-adic valuation of the counting function of the
alternating sign matrices. We find an exact analytic
expression for it that exhibits the fluctuating
behavior, by means of Fourier coefficients. The method
is the Mellin--Perron technique, which is familiar in
the analysis of the sum-of-digits function and related
quantities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhang:2011:FPM,
author = "Deyu Zhang and Wenguang Zhai",
title = "On the fifth-power moment of {$ \Delta (x) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "71--86",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003922",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003922",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Buckingham:2011:FGI,
author = "Paul Buckingham",
title = "The Fractional {Galois} Ideal for Arbitrary Order of
Vanishing",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "87--99",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004010",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004010",
abstract = "We propose a candidate, which we call the fractional
Galois ideal after Snaith's fractional ideal, for
replacing the classical Stickelberger ideal associated
to an abelian extension of number fields. The
Stickelberger ideal can be seen as gathering
information about those {$L$}-functions of the
extension which are non-zero at the special point s =
0, and was conjectured by Brumer to give annihilators
of class-groups viewed as Galois modules. An earlier
version of the fractional Galois ideal extended the
Stickelberger ideal to include {$L$}-functions with a
simple zero at s = 0, and was shown by the present
author to provide class-Group annihilators not existing
in the Stickelberger ideal. The version presented in
this paper deals with {$L$}-functions of arbitrary
order of vanishing at s = 0, and we give evidence using
results of Popescu and Rubin that it is closely related
to the Fitting ideal of the class-group, a canonical
ideal of annihilators. Finally, we prove an equality
involving Stark elements and class-groups originally
due to B{\"u}y{\"u}kboduk, but under a slightly
different assumption, the advantage being that we need
none of the Kolyvagin system machinery used in the
original proof.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gurak:2011:GKS,
author = "S. Gurak",
title = "{Gauss} and {Kloosterman} Sums Over Residue Rings of
Algebraic Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "101--114",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003958",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003958",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bremner:2011:RPS,
author = "Andrew Bremner and Maciej Ulas",
title = "Rational Points on Some Hyper- and Superelliptic
Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "115--132",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003946",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003946",
abstract = "We construct families of certain hyper- and
superelliptic curves that contain a (small) number of
rational points. This leads to lower bounds for the
ranks of Jacobians of certain high genus curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fu:2011:CPO,
author = "Shishuo Fu",
title = "Combinatorial Proof of One Congruence for the Broken
$1$-Diamond Partition and a Generalization",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "133--144",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004022",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004022",
abstract = "In one of their recent collaborative papers, Andrews
and Paule continue their study of partition functions
via MacMahon's Partition Analysis by considering
partition functions associated with directed graphs
which consist of chains of diamond shape. They prove a
congruence related to one of these partition functions
and conjecture a number of similar congruence results.
In this note, we reprove this congruence by
constructing an explicit way to group partitions. Then
we keep the essence of the method and manage to apply
it to a different kind of plane partitions to get more
general results and several other congruences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cosgrave:2011:MOC,
author = "John B. Cosgrave and Karl Dilcher",
title = "The Multiplicative Orders of Certain {Gauss}
Factorials",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "145--171",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100396X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100396X",
abstract = "A theorem of Gauss extending Wilson's theorem states
the congruence (n - 1)$_n$ ! \equiv -1 (mod n) whenever
n has a primitive root, and \equiv 1 (mod n) otherwise,
where N$_n$ ! denotes the product of all integers up to
N that are relatively prime to n. In the spirit of this
theorem, we study the multiplicative orders of (mod n)
for odd prime powers p$^{\alpha }$. We prove a general
result about the connection between the order for
p$^{\alpha }$ and for p$^{\alpha + 1}$ and study
exceptions to the general rule. Particular emphasis is
given to the cases M = 3, M = 4 and M = 6, while the
case M = 2 is already known.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Carls:2011:GTC,
author = "Robert Carls",
title = "{Galois} Theory of the Canonical Theta Structure",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "173--202",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003934",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/agm.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003934",
abstract = "In this article, we give a Galois-theoretic
characterization of the canonical theta structure. The
Galois property of the canonical theta structure
translates into certain $p$-adic theta relations which
are satisfied by the canonical theta null point of the
canonical lift. As an application, we prove some 2-adic
theta identities which describe the set of canonical
theta null points of the canonical lifts of ordinary
abelian varieties in characteristic 2. The latter theta
relations are suitable for explicit canonical lifting.
Using the theory of canonical theta null points, we are
able to give a theoretical foundation to Mestre's point
counting algorithm which is based on the computation of
the generalized arithmetic geometric mean sequence.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hubrechts:2011:MEH,
author = "Hendrik Hubrechts",
title = "Memory Efficient Hyperelliptic Curve Point Counting",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "203--214",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004034",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004034",
abstract = "In recent algorithms that use deformation in order to
compute the number of points on varieties over a finite
field, certain differential equations of matrices over
$p$-adic fields emerge. We present a novel strategy to
solve this kind of equations in a memory efficient way.
The main application is an algorithm requiring
quasi-cubic time and only quadratic memory in the
parameter n, that solves the following problem: for E a
hyperelliptic curve of genus g over a finite field of
extension degree n and small characteristic, compute
its zeta function. This improves substantially upon
Kedlaya's result which has the same quasi-cubic time
asymptotic, but requires also cubic memory size.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Boulet:2011:SMD,
author = "Cilanne Boulet and Ka{\u{g}}an Kur{\c{s}}ung{\"o}z",
title = "Symmetry of $k$-marked {Durfee} symbols",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "215--230",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003971",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003971",
abstract = "Andrews introduced the k-marked Durfee symbols in his
work defining a variant of the Atkin--Garvan moments of
ranks. He provided and proved many identities and
congruences using analytical methods. Here, we give an
equivalent description of k-marked Durfee symbols, and
using it we give combinatorial proofs to two results of
Andrews'.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Brink:2011:RFD,
author = "David Brink",
title = "{R{\'e}dei} Fields and Dyadic Extensions",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "231--240",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003983",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003983",
abstract = "For an arbitrary non-square discriminant D, the {\em
R{\'e}dei field\/} \Gamma$_0$ (D) is introduced as an
extension of analogous to the genus field and connected
with the R{\'e}dei--Reichardt Theorem. It is shown how
to compute R{\'e}dei fields, and this is used to find
socles of dyadic extensions of K for negative D.
Finally, a theorem and two conjectures are presented
relating the fields and for an odd prime p.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Li:2011:WWL,
author = "Xiaoqing Li",
title = "A Weighted {Weyl} Law for the Modular Surface",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "241--248",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111003995",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003995",
abstract = "In this paper, we will prove a Weyl law for the
modular surface weighted by the first Fourier
coefficient of the Maass cusp forms. Our error term
corresponds to the best known error term in the Weyl
law and improves a previous result of Kuznetsov.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baba:2011:OSM,
author = "Srinath Baba and H{\aa}kan Granath",
title = "Orthogonal Systems of Modular Forms and Supersingular
Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "1",
pages = "249--259",
month = feb,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004009",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004009",
abstract = "We extend a construction of Kaneko and Zagier to
obtain modular forms which, modulo a prime, vanish at
the supersingular points. These modular forms arise
simultaneously as solutions of certain second-order
differential equations, and as an orthogonal basis for
an inner product on the space of modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Carter:2011:BGP,
author = "Andrea C. Carter",
title = "The {Brauer} Group of {Del Pezzo} Surfaces",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "261--287",
month = mar,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111003910",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111003910",
abstract = "Let S$_1$ be a Del Pezzo surface of degree 1 over a
number field k. We establish a criterion for the
existence of a nontrivial element of order 5 in the
Brauer group of S$_1$ in terms of certain Galois-stable
configurations of exceptional divisors on this
surface.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Roberts:2011:NPF,
author = "David P. Roberts",
title = "Nonsolvable Polynomials with Field Discriminant {$ 5^A
$}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "289--322",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004113",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004113",
abstract = "We present the first explicitly known polynomials in
Z[x] with nonsolvable Galois group and field
discriminant of the form \pm p$^A$ for p \leq 7 a
prime. Our main polynomial has degree 25, Galois group
of the form PSL$_2$ (5)$^5$. 10, and field discriminant
5$^{69}$. A closely related polynomial has degree 120,
Galois group of the form SL$_2$ (5)$^5$. 20, and field
discriminant 5$^{311}$. We completely describe 5-adic
behavior, finding in particular that the root
discriminant of both splitting fields is 125 \cdotp
5$^{-1 / 12500}$ \approx 124.984 and the class number
of the latter field is divisible by 5$^4$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Murty:2011:TCI,
author = "M. Ram Murty and Chester J. Weatherby",
title = "On the Transcendence of Certain Infinite Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "323--339",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004058",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004058",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Barcau:2011:CCF,
author = "Mugurel Barcau and Vicen{\c{t}}iu Pa{\c{s}}ol",
title = "$ \bmod p $ congruences for cusp forms of weight four
for {$ \Gamma_0 (p N) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "341--350",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100406X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100406X",
abstract = "In [1], the authors prove a conjecture of Calegari and
Stein regarding $ \bmod p $ congruences between cusp
forms of weight four for \Gamma$_0$ (p) and the
derivatives of cusp forms of weight two for the same
congruence subgroup. In this paper, we investigate
whether or not the result remains valid for cusp forms
of level N$_p$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Muic:2011:NVC,
author = "Goran Mui{\'c}",
title = "On the Non-Vanishing of Certain Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "351--370",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004083",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004083",
abstract = "Let \Gamma \subset SL$_2$ ({\mathbb{R}}) be a Fuchsian
group of the first kind. In this paper, we study the
non-vanishing of the spanning set for the space of
cuspidal modular forms of weight m \geq 3 constructed
in [5, Corollary 2.6.11]. Our approach is based on the
generalization of the non-vanishing criterion for L$^1$
Poincar{\'e} series defined for locally compact groups
and proved in [6, Theorem 4.1]. We obtain very sharp
bounds for the non-vanishing of the spaces of cusp
forms for general \Gamma having at least one cusp. We
obtain explicit results for congruence subgroups \Gamma
(N), \Gamma$_0$ (N), and \Gamma$_1$ (N) (N \geq 1).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bui:2011:CVD,
author = "H. M. Bui and Micah B. Milinovich",
title = "Central Values of Derivatives of {Dirichlet}
{$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "371--388",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004125",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004125",
abstract = "Let be the set of even, primitive Dirichlet characters
(mod q). Using the mollifier method, we show that
L$^{(k)}$ (\frac{1}{2}, \chi) \neq 0 for almost all the
characters when k and q are large. Here L(s, \chi) is
the Dirichlet {$L$}-function associated to the
character \chi.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Martin:2011:RTF,
author = "Kimball Martin and Mark McKee and Eric Wambach",
title = "A Relative Trace Formula for a Compact {Riemann}
Surface",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "389--429",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004101",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004101",
abstract = "We study a relative trace formula for a compact
Riemann surface with respect to a closed geodesic C.
This can be expressed as a relation between the period
spectrum and the ortholength spectrum of C. This
provides a new proof of asymptotic results for both the
periods of Laplacian eigenforms along C as well
estimates on the lengths of geodesic segments which
start and end orthogonally on C. Variant trace formulas
also lead to several simultaneous nonvanishing results
for different periods.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bundschuh:2011:AND,
author = "Peter Bundschuh and Keijo V{\"a}{\"a}n{\"a}nen",
title = "An application of {Nesterenko}'s dimension estimate to
$p$-adic $q$-series",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "431--447",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004071",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004071",
abstract = "Very recently, Nesterenko proved a $p$-adic analogue
of his famous dimension estimate from 1985. The main
aim of our present paper is to use this criterion to
obtain lower bounds for the dimension of {$ \mathbb
{Q}$}-vector spaces spanned by the values at certain
rational points of $p$-adic solutions of a class of
linear q-difference equations. For the application of
Nesterenko's new estimate, we first need a $p$-adic
analogue of T{\"o}pfer's results on entire solutions of
such functional equations, and secondly, very precise
evaluations of certain $p$-adic Schnirelman
integrals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zorn:2011:EDI,
author = "Christian Zorn",
title = "Explicit doubling integrals for {$ \mathrm {Sp}_2 (F)
$} and {$ \widetilde {\mathrm {Sp}_2}(F) $} using
``good test vectors''",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "449--527",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004046",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004046",
abstract = "In this paper, we offer some explicit computations of
a formulation of the doubling method of
Piatetski-Shapiro and Rallis for the groups Sp$_2$ (F)
(the rank 2 symplectic group) and its metaplectic cover
for F a finite extension of {$ \mathbb {Q}$}$_p$ with p
\neq 2. We determine a set of ``good test vectors'' for
the irreducible constituents of unramified principal
series representations for these groups as well as a
set of ``good theta test sections'' in a family of
degenerate principal series representations of Sp$_4$
(F) and . Determining ``good test data'' that produces
a non-vanishing doubling integral should indicate the
existence of a non-vanishing theta lifts for dual pairs
of the type (Sp$_2$ (F), O(V)) (respectively) where V
is a quadratic space of an even (respectively odd)
dimension.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mori:2011:PSE,
author = "Andrea Mori",
title = "Power Series Expansions of Modular Forms and Their
Interpolation Properties",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "2",
pages = "529--577",
month = mar,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004095",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004095",
abstract = "We define a power series expansion of an holomorphic
modular form $f$ in the $p$-adic neighborhood of a CM
point $x$ of type $K$ for a split good prime $p$. The
modularity group can be either a classical conguence
group or a group of norm $1$ elements in an order of an
indefinite quaternion algebra. The expansion
coefficients are shown to be closely related to the
classical Maass operators and give $p$-adic information
on the ring of definition of $f$. By letting the CM
point $x$ vary in its Galois orbit, the $r$-th
coefficients define a $p$-adic $ K^\times $-modular
form in the sense of Hida. By coupling this form with
the $p$-adic avatars of algebraic Hecke characters
belonging to a suitable family and using a
Rankin--Selberg type formula due to Harris and Kudla
along with some explicit computations of Watson and of
Prasanna, we obtain in the even weight case a $p$-adic
measure whose moments are essentially the square roots
of a family of twisted special values of the
automorphic $L$-function associated with the base
change of $f$ to $K$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pollack:2011:ESP,
author = "Paul Pollack",
title = "The Exceptional Set in the Polynomial {Goldbach}
Problem",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "579--591",
month = may,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111004423",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004423",
abstract = "For each natural number N, let R(N) denote the number
of representations of N as a sum of two primes. Hardy
and Littlewood proposed a plausible asymptotic formula
for R(2N) and showed, under the assumption of the
Riemann Hypothesis for Dirichlet {$L$}-functions, that
the formula holds ``on average'' in a certain sense.
From this they deduced (under ERH) that all but
O$_{\epsilon }$ (x$^{1 / 2 + \epsilon }$) of the even
natural numbers in [1, x] can be written as a sum of
two primes. We generalize their results to the setting
of polynomials over a finite field. Owing to Weil's
Riemann Hypothesis, our results are unconditional.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bugeaud:2011:MCC,
author = "Yann Bugeaud and Alan Haynes and Sanju Velani",
title = "Metric Considerations Concerning the Mixed
{Littlewood} Conjecture",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "593--609",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004289",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004289",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Draziotis:2011:NIP,
author = "Konstantinos A. Draziotis",
title = "On the number of integer points on the elliptic curve
{$ y^2 = x^3 + A x $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "611--621",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004149",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004149",
abstract = "It is given an upper bound for the number of the
integer points of the elliptic curve y$^2$ = x$^3$ + Ax
(A \in {\mathbb{Z}}) and a conjecture of Schmidt is
proven for this family of elliptic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Medina:2011:IPL,
author = "Luis A. Medina and Victor H. Moll and Eric S.
Rowland",
title = "Iterated Primitives of Logarithmic Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "623--634",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100423X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100423X",
abstract = "The evaluation of iterated primitives of powers of
logarithms is expressed in closed form. The expressions
contain polynomials with coefficients given in terms of
the harmonic numbers and their generalizations. The
logconcavity of these polynomials is established.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ziegler:2011:AUS,
author = "Volker Ziegler",
title = "The Additive {$S$}-Unit Structure of Quadratic
Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "635--644",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004216",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004216",
abstract = "We consider a variation of the unit sum number problem
for quadratic fields and prove various results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sun:2011:SNC,
author = "Zhi-Wei Sun and Roberto Tauraso",
title = "On Some New Congruences for Binomial Coefficients",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "645--662",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004393",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004393",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Astaneh-Asl:2011:IHP,
author = "Ali Astaneh-Asl and Hassan Daghigh",
title = "Independence of {Heegner} Points for Nonmaximal
Orders",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "663--669",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004241",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004241",
abstract = "The independence of Heegner points associated to
distinct imaginary quadratic fields has been shown by
Rosen and Silverman. In this paper we show the
independence of Heegner points associated to orders
with the same conductor in distinct imaginary quadratic
fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gekeler:2011:ZDD,
author = "Ernst-Ulrich Gekeler",
title = "Zero Distribution and Decay at Infinity of {Drinfeld}
Modular Coefficient Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "671--693",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004307",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004307",
abstract = "Let \Gamma = GL(2, {$ \mathbb {F} $}$_q$ [T]) be the
Drinfeld modular group, which acts on the rigid
analytic upper half-plane \Omega. We determine the
zeroes of the coefficient modular forms$_a$ \ell$_k$ on
the standard fundamental domain for \Gamma on \Omega,
along with the dependence of |$_a$ \ell$_k$ (z)| on.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Widmer:2011:NFN,
author = "Martin Widmer",
title = "On Number Fields with Nontrivial Subfields",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "695--720",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004204",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004204",
abstract = "What is the probability for a number field of
composite degree d to have a nontrivial subfield? As
the reader might expect the answer heavily depends on
the interpretation of probability. We show that if the
fields are enumerated by the smallest height of their
generators the probability is zero, at least if d > 6.
This is in contrast to what one expects when the fields
are enumerated by the discriminant. The main result of
this paper is an estimate for the number of algebraic
numbers of degree d = en and bounded height which
generate a field that contains an unspecified subfield
of degree e. If n > {maxe$^2$ + e, 10}, we get the
correct asymptotics as the height tends to infinity.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Maire:2011:PLE,
author = "Christian Maire",
title = "Plongements locaux et extensions de corps de nombres.
({French}) [{Local} embeddings and number field
extensions]",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "721--738",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004332",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004332",
abstract = "Dans ce travail, nous nous int{\'e}ressons au
plongement des T-unit{\'e}s d'un corps de nombres K
dans une partie de ses compl{\'e}t{\'e}s $p$-adiques
construite sur l'ensemble S. Nous montrons que
l'injectivit{\'e} de permet d'obtenir des informations
sur la structure du groupe de Galois de certaines
extensions de K o{\`u} la ramification est li{\'e}e
{\`a} S et la d{\'e}composition {\`a} T. Nous
{\'e}tudions {\'e}galement le comportement asymptotique
du noyau de le long d'une extension $p$-adique
analytique sans $p$-torsion. In this article, we are
interested in the embedding of the T-units of a number
field K in some part of its $p$-adic completions at S.
We show that the injectivity of allows us to obtain
some information on the structure of the Galois group
of some extensions of K where the ramification is
attached at S and the decomposition at T. Moreover, we
study the asymptotic behavior of the kernel along a
$p$-adic analytic extension.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Zywina:2011:RKC,
author = "David Zywina",
title = "A Refinement of {Koblitz}'s Conjecture",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "739--769",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004411",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004411",
abstract = "Let E be an elliptic curve over the rationals. In
1988, Koblitz conjectured an asymptotic for the number
of primes $p$ for which the cardinality of the group of
{$ \mathbb {F} $}$_p$-points of $E$ is prime. However,
the constant occurring in his asymptotic does not take
into account that the distributions of the $ |E(\mathbb
{F}_p)|$ need not be independent modulo distinct
primes. We shall describe a corrected constant. We also
take the opportunity to extend the scope of the
original conjecture to ask how often $ |E(\mathbb
{F}_p)| / t$ is an integer and prime for a fixed
positive integer $t$, and to consider elliptic curves
over arbitrary number fields. Several worked out
examples are provided to supply numerical evidence for
the new conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Odzak:2011:IFG,
author = "Almasa Od{\v{z}}ak and Lejla Smajlovi{\'c}",
title = "On interpolation functions for generalized {Li}
coefficients in the {Selberg} class",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "771--792",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004356",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004356",
abstract = "We prove that there exists an entire complex function
of order one and finite exponential type that
interpolates the Li coefficients \lambda$_F$ (n)
attached to a function F in the class that contains
both the Selberg class of functions and
(unconditionally) the class of all automorphic
{$L$}-functions attached to irreducible, cuspidal,
unitary representations of GL$_n$ ({$ \mathbb {Q}$}).
We also prove that the interpolation function is
(essentially) unique, under generalized Riemann
hypothesis. Furthermore, we obtain entire functions of
order one and finite exponential type that interpolate
both archimedean and non-archimedean contribution to
\lambda$_F$ (n) and show that those functions can be
interpreted as zeta functions built, respectively, over
trivial zeros and all zeros of a function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kaavya:2011:CPP,
author = "S. J. Kaavya",
title = "Crank $0$ Partitions and the Parity of the Partition
Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "793--801",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004381",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004381",
abstract = "A well-known problem regarding the integer partition
function p(n) is the {\em parity problem\/}, how often
is p(n) even or odd? Motivated by this problem, we
obtain the following results: (1) A generating function
for the number of crank 0 partitions of n. (2) An
involution on the crank 0 partitions whose fixed points
are called {\em invariant\/} partitions. We then derive
a generating function for the number of invariant
partitions. (3) A generating function for the number of
self-conjugate rank 0 partitions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gallegos-Ruiz:2011:IPH,
author = "Homero R. Gallegos-Ruiz",
title = "{$S$}-integral points on hyperelliptic curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "803--824",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004435",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004435",
abstract = "Let C : Y$^2$ = a$_n$ X$^n$ + \cdots + a$_0$ be a
hyperelliptic curve with the a$_i$ rational integers, n
\geq 5, and the polynomial on the right irreducible.
Let J be its Jacobian. Let S be a finite set of
rational primes. We give a completely explicit upper
bound for the size of the S-integral points on the
model C, provided we know at least one rational point
on C and a Mordell--Weil basis for J({$ \mathbb {Q}$}).
We use a refinement of the Mordell--Weil sieve which,
combined with the upper bound, is capable of
determining all the S-integral points. The method is
illustrated by determining the S-integral points on the
genus 2 hyperelliptic model Y$^2$- Y = X$^5$ X for the
set S of the first 22 primes.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bringmann:2011:EFC,
author = "Kathrin Bringmann and Olav K. Richter",
title = "Exact Formulas for Coefficients of {Jacobi} Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "825--833",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004617",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004617",
abstract = "In previous work, we introduced harmonic Maass--Jacobi
forms. The space of such forms includes the classical
Jacobi forms and certain Maass--Jacobi--Poincar{\'e}
series, as well as Zwegers' real-analytic Jacobi forms,
which play an important role in the study of mock theta
functions and related objects. Harmonic Maass--Jacobi
forms decompose naturally into holomorphic and
non-holomorphic parts. In this paper, we give exact
formulas for the Fourier coefficients of the
holomorphic parts of harmonic Maass--Jacobi forms and,
in particular, we obtain explicit formulas for the
Fourier coefficients of weak Jacobi forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Meemark:2011:DSM,
author = "Yotsanan Meemark and Nawaphon Maingam",
title = "The Digraph of the Square Mapping on Quotient Rings
Over the {Gaussian} Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "835--852",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004459",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004459",
abstract = "In this work, we investigate the structure of the
digraph associated with the square mapping on the ring
of Gaussian integers by using the exponent of the unit
group modulo \gamma. The formula for the fixed points
of is established. Some connections of the lengths of
cycles with the exponent of the unit group modulo
\gamma are presented. Furthermore, we study the maximum
distance from the cycle on each component.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Han:2011:APF,
author = "Jeong Soon Han and Hee Sik Kim and J. Neggers",
title = "Acknowledgment of priority: {``The Fibonacci-norm of a
positive integer: Observations and conjectures''}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "3",
pages = "853--854",
month = may,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004927",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See \cite{Han:2010:FNP}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004927",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Flicker:2011:CFP,
author = "Yuval Z. Flicker",
title = "Cusp forms on {$ \mathrm {GSp}(4) $} with {$ \mathrm
{SO}(4) $}-periods",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "855--919",
month = jun,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111004186",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004186",
abstract = "The Saito--Kurokawa lifting of automorphic
representations from PGL(2) to the projective
symplectic group of similitudes PGSp(4) of genus 2 is
studied using the Fourier summation formula (an
instance of the ``relative trace formula''), thus
characterizing the image as the representations with a
nonzero period for the special orthogonal group SO(4,
E/F) associated to a quadratic extension E of the
global base field F, and a nonzero Fourier coefficient
for a generic character of the unipotent radical of the
Siegel parabolic subgroup. The image is nongeneric and
almost everywhere nontempered, violating a naive
generalization of the Ramanujan conjecture. Technical
advances here concern the development of the summation
formula and matching of relative orbital integrals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Schwartz:2011:SAP,
author = "Ryan Schwartz and J{\'o}zsef Solymosi and Frank {De
Zeeuw}",
title = "Simultaneous Arithmetic Progressions on Algebraic
Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "921--931",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004198",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004198",
abstract = "A {\em simultaneous arithmetic progression\/} (s.a.p.)
of length k consists of k points (x$_i$, y$_{\sigma
(i)}$), where and are arithmetic progressions and
\sigma is a permutation. Garcia-Selfa and Tornero asked
whether there is a bound on the length of an s.a.p. on
an elliptic curve in Weierstrass form over {$ \mathbb
{Q}$}. We show that 4319 is such a bound for curves
over {\mathbb{R}}. This is done by considering
translates of the curve in a grid as a graph. A simple
upper bound is found for the number of crossings and
the ``crossing inequality'' gives a lower bound.
Together these bound the length of an s.a.p. on the
curve. We also extend this method to bound the k for
which a real algebraic curve can contain k points from
a k $ \times $ k grid. Lastly, these results are
extended to complex algebraic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Griffin:2011:DPC,
author = "Michael Griffin",
title = "Divisibility Properties of Coefficients of Weight $0$
Weakly Holomorphic Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "933--941",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004599",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004599",
abstract = "In 1949, Lehner showed that certain coefficients of
the modular invariant j(\tau) are divisible by high
powers of small primes. Kolberg refined Lehner's
results and proved congruences for these coefficients
modulo high powers of these primes. We extend Lehner's
and Kolberg's work to the elements of a canonical basis
for the space of weight 0 weakly holomorphic modular
forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hohn:2011:TGR,
author = "Gerald H{\"o}hn",
title = "On a Theorem of {Garza} Regarding Algebraic Numbers
with Real Conjugates",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "943--945",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004320",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004320",
abstract = "We give a new proof of a theorem on the height of
algebraic numbers with real conjugates.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Elsenhans:2011:CSG,
author = "Andreas-Stephan Elsenhans and J{\"o}rg Jahnel",
title = "Cubic Surfaces with a {Galois} Invariant Pair of
{Steiner} Trihedra",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "947--970",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004253",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004253",
abstract = "We present a method to construct non-singular cubic
surfaces over {$ \mathbb {Q} $} with a Galois invariant
pair of Steiner trihedra. We start with cubic surfaces
in a form generalizing that of Cayley and Salmon. For
these, we develop an explicit version of Galois
descent.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Saha:2011:PDR,
author = "Abhishek Saha",
title = "Prime Density Results for {Hecke} Eigenvalues of a
{Siegel} Cusp Form",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "971--979",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004642",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004642",
abstract = "Let F \in S$_k$ (Sp(2g, {\mathbb{Z}})) be a cuspidal
Siegel eigenform of genus g with normalized Hecke
eigenvalues \mu$_F$ (n). Suppose that the associated
automorphic representation \pi$_F$ is locally tempered
everywhere. For each c > 0, we consider the set of
primes p for which |\mu$_F$ (p)| \geq c and we provide
an explicit upper bound on the density of this set. In
the case g = 2, we also provide an explicit upper bound
on the density of the set of primes p for which \mu$_F$
(p) \geq c.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Miyazaki:2011:TCE,
author = "Takafumi Miyazaki",
title = "{Terai}'s Conjecture on Exponential {Diophantine}
Equations",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "981--999",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004496",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004496",
abstract = "Let a, b, c be relatively prime positive integers such
that a$^p$ + b$^q$ = c$^r$ with fixed integers p, q, r
\geq 2. Terai conjectured that the equation a$^x$ +
b$^y$ = c$^z$ has no positive integral solutions other
than (x, y, z) = (p, q, r) except for specific cases.
Most known results on this conjecture concern the case
where p = q = 2 and either r = 2 or odd r \geq 3. In
this paper, we consider the case where p = q = 2 and r
> 2 is even, and partially verify Terai's conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Billerey:2011:CIP,
author = "Nicolas Billerey",
title = "Crit{\`e}res d'irr{\'e}ductibilit{\'e} pour les
repr{\'e}sentations des courbes elliptiques. ({French})
[{Irreducibility} criteria for the representations of
elliptic curves]",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1001--1032",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004538",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004538",
abstract = "Soit E une courbe elliptique d{\'e}finie sur un corps
de nombres K. On dit qu'un nombre premier p est
r{\'e}ductible pour le couple (E, K) si E admet une
$p$-isog{\'e}nie d{\'e}finie sur K. L'ensemble de tous
ces nombres premiers est fini si et seulement si E n'a
pas de multiplication complexe d{\'e}finie sur K. Dans
cet article, on montre que l'ensemble des nombres
premiers r{\'e}ductibles pour le couple (E, K) est
contenu dans l'ensemble des diviseurs premiers d'une
liste explicite d'entiers (d{\'e}pendant de E et de K)
dont une infinit{\'e} d'entre eux est non nulle. Cela
fournit un algorithme efficace de calcul dans le cas
fini. D'autres crit{\`e}res moins g{\'e}n{\'e}raux,
mais n{\'e}anmoins utiles sont donn{\'e}s ainsi que de
nombreux exemples num{\'e}riques. Let E be an elliptic
curve defined over a number field K. We say that a
prime number p is reducible for (E, K) if E admits a
$p$-isogeny defined over K. The so-called reducible set
of all such prime numbers is finite if and only if E
does not have complex multiplication over K. In this
paper, we prove that the reducible set is included in
the set of prime divisors of an explicit list of
integers (depending on E and K), infinitely many of
them being non-zero. It provides an efficient algorithm
for computing it in the finite case. Other less general
but rather useful criteria are given, as well as many
numerical examples.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Hassen:2011:ZFR,
author = "Abdul Hassen and Hieu D. Nguyen",
title = "A Zero-Free Region for Hypergeometric Zeta Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1033--1043",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004678",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004678",
abstract = "This paper investigates the location of ``trivial''
zeros of some hypergeometric zeta functions. Analogous
to Riemann's zeta function, we demonstrate that they
possess a zero-free region on a left-half complex
plane, except for infinitely many zeros regularly
spaced on the negative real axis.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ghosh:2011:KGT,
author = "Anish Ghosh",
title = "A {Khintchine--Groshev} theorem for affine
hyperplanes",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1045--1064",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004228",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004228",
abstract = "We prove the divergence case of the
Khintchine--Groshev theorem for a large class of affine
hyperplanes, completing the convergence case proved in
[11] and answering in part a question of Beresnevich
{\em et al.\/} ([4]). We use the mechanism of regular
systems developed in [4] and estimates from [11].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gun:2011:AIV,
author = "Sanoli Gun and M. Ram Murty and Purusottam Rath",
title = "Algebraic Independence of Values of Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1065--1074",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004769",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004769",
abstract = "We investigate values of modular forms with algebraic
Fourier coefficients at algebraic arguments. As a
consequence, we conclude about the nature of zeros of
such modular forms. In particular, the singular values
of modular forms (that is, values at CM points) are
related to the recent work of Nesterenko. As an
application, we deduce the transcendence of critical
values of certain Hecke $L$-series. We also discuss how
these investigations generalize to the case of
quasi-modular forms with algebraic Fourier
coefficients.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mera:2011:ZFR,
author = "Mitsugu Mera",
title = "Zero-free regions of a $q$-analogue of the complete
{Riemann} zeta function",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1075--1092",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004344",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004344",
abstract = "A q-analogue of the complete Riemann zeta function
presented in this paper is defined by the q-Mellin
transform of the Jacobi theta function. We study
zero-free regions of the q-zeta function. As a
by-product, we show that the Riemann zeta function does
not vanish in a sub-region of the critical strip.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cao:2011:SDR,
author = "Wei Cao",
title = "A Special Degree Reduction of Polynomials Over Finite
Fields with Applications",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1093--1102",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004277",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004277",
abstract = "Let f be a polynomial in n variables over the finite
field {$ \mathbb {F} $}$_q$ and N$_q$ (f) denote the
number of {$ \mathbb {F} $}$_q$-rational points on the
affine hypersurface f = 0 in {$ \mathbb {A} $}$^n$ ({$
\mathbb {F} $}$_q$). A \phi -reduction of f is defined
to be a transformation \sigma : {$ \mathbb {F} $}$_q$
[x$_1$, \ldots, x$_n$ ] \rightarrow {$ \mathbb {F}
$}$_q$ [x$_1$, \ldots, x$_n$ ] such that N$_q$ (f) =
N$_q$ (\sigma(f)) and deg f \geq deg \sigma(f). In this
paper, we investigate \phi -reduction by using the
degree matrix which is formed by the exponents of the
variables of f. With \phi -reduction, we may improve
various estimates on N$_q$ (f) and utilize the known
results for polynomials with low degree. Furthermore,
it can be used to find the explicit formula for N$_q$
(f).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Raji:2011:ECT,
author = "Wissam Raji",
title = "{Eichler} Cohomology Theorem for Generalized Modular
Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "4",
pages = "1103--1113",
month = jun,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004514",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004514",
abstract = "We show starting with relations between Fourier
coefficients of weakly parabolic generalized modular
forms of negative weight that we can construct
automorphic integrals for large integer weights. We
finally prove an Eichler isomorphism theorem for weakly
parabolic generalized modular forms using the classical
approach as in [3].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Freiman:2011:SSC,
author = "Gregory A. Freiman and Yonutz V. Stanchescu",
title = "Sets with Several Centers of Symmetry",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1115--1135",
month = aug,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111004174",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004174",
abstract = "Let A be a finite subset of the group
{\mathbb{Z}}$^2$. Let C = {c$_0$, c$_1$, \ldots, c$_{s
- 1}$ } be a finite set of s distinct points in the
plane. For every 0 \leq i \leq s -1, we define D$_i$ =
{a - a\prime : a \in A, a\prime \in A, a + a\prime =
2c$_i$ } and R$_s$ (A) = |D$_0$ \cup D$_1$ \cup \ldots
\cup D$_{s - 1}$ |. In [1, 2], we found the maximal
value of R$_s$ (A) in cases s = 1, s = 2 and s = 3 and
studied the structure of A assuming that R$_3$ (A) is
equal or close to its maximal value. In this paper, we
examine the case of s = 4 centers of symmetry and we
find the {\em maximal value\/} of R$_4$ (A). Moreover,
in cases when the maximal value is attained, we will
describe the {\em structure of extremal sets}.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tu:2011:ONA,
author = "Fang-Ting Tu",
title = "On Orders of {$ M(2, K) $} Over a Non--{Archimedean}
Local Field",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1137--1149",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004654",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004654",
abstract = "Let K be a non-Archimedean local field. In this paper,
we first show that if an order in M(2, K) is the
intersection of (finitely many) maximal orders in M(2,
K), then it is the intersection of at most three
maximal orders. Using this result, we obtain a complete
classification of orders in M(2, K) that are
intersections of maximal orders.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dixit:2011:ATF,
author = "Atul Dixit",
title = "Analogues of a Transformation Formula of {Ramanujan}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1151--1172",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100454X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100454X",
abstract = "We derive two new analogues of a transformation
formula of Ramanujan involving the Gamma function and
Riemann zeta function present in his \booktitle{Lost
Notebook}. Both involve infinite series consisting of
Hurwitz zeta functions and yield modular-type
relations. As a special case of the first formula, we
obtain an identity involving polygamma functions given
by A. P. Guinand and as a limiting case of the second
formula, we derive the transformation formula of
Ramanujan.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ayad:2011:CDV,
author = "Mohamed Ayad and Omar Kihel",
title = "Common Divisors of Values of Polynomials and Common
Factors of Indices in a Number Field",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1173--1194",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004526",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004526",
abstract = "Let K be a number field of degree n over {$ \mathbb
{Q} $}, {\^A} be the set of integers of K that are
primitive over {$ \mathbb {Q} $} and let I(K) be its
index. The prime factors of I(K) are called common
factors of indices or inessential discriminant
divisors. We show that these primes divide another
index i(K) previously defined by Gunji and McQuillan as
i(K) = lcm$_{\theta \in {\^ A}}$ i(\theta), where
i(\theta) = gcd$_{x \in {\mathbb {Z}}}$ F$_{\theta }$
(x) and F$_{\theta }$ (x) is the characteristic
polynomial of \theta over {$ \mathbb {Q}$}. It is shown
that there exists \theta \in {\^A} such that i(K) =
i(\theta) and an algorithm is given for the computation
of such an integer. For any prime p|i(K), an integer
\rho$_K$ (p) defined as the number of such that
p|i(\theta) is investigated. It is shown that this
integer determines in some cases the splitting type of
p in K. Some open questions related to I(K), i(K) and
\rho$_K$ (p) are stated.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Philippon:2011:AFC,
author = "Patrice Philippon",
title = "Approximations fonctionnelles des courbes des espaces
projectifs. ({French}) [{Functional} approximations of
the curves of projective spaces]",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1195--1215",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004502",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004502",
abstract = "Algebraic approximation to points in projective spaces
offers a new and more flexible approach to algebraic
independence theory. When working over the field of
algebraic numbers, it leads to open conjectures in
higher dimension extending known results in Diophantine
approximation. We show here that over the algebraic
closure of a function field in one variable, the analog
of these conjectures is true. We also derive transfer
lemmas which have applications in the study of
multiplicity estimates, for example.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Dubickas:2011:RPD,
author = "Art{\=u}ras Dubickas",
title = "Roots of Polynomials with Dominant Term",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1217--1228",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004575",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004575",
abstract = "We characterize all algebraic numbers which are roots
of integer polynomials with a coefficient whose modulus
is greater than or equal to the sum of moduli of all
the remaining coefficients. It turns out that these
numbers are zero, roots of unity and those algebraic
numbers \beta whose conjugates over {$ \mathbb {Q} $}
(including \beta itself) do not lie on the circle |z| =
1. We also describe all algebraic integers with norm B
which are roots of an integer polynomial with constant
coefficient B and the sum of moduli of all other
coefficients at most |B|. In contrast to the above, the
set of such algebraic integers is ``quite small''.
These results are motivated by a recent paper of
Frougny and Steiner on the so-called minimal weight
\beta -expansions and are also related to some work on
canonical number systems and tilings.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Boylan:2011:VFC,
author = "Matthew Boylan and Sharon Anne Garthwaite and John
Webb",
title = "On the Vanishing of {Fourier} Coefficients of Certain
Genus Zero Newforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1229--1245",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004290",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004290",
abstract = "Given a classical modular form f(z), a basic question
is whether any of its Fourier coefficients vanish. This
question remains open for certain modular forms. For
example, let \Delta (z) = \Sigma \Gamma (n)q$^n$ \in
S$_{12}$ (\Gamma$_0$ (1)). A well-known conjecture of
Lehmer asserts that \tau (n) \neq 0 for all n. In
recent work, Ono constructed a family of polynomials
A$_n$ (x) \in {$ \mathbb {Q}$}[x] with the property
that \tau (n) vanishes if and only if A$_n$ (0) and
A$_n$ (1728) do. In this paper, we establish a similar
criterion for the vanishing of coefficients of certain
newforms on genus zero groups of prime level.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ghitza:2011:DHE,
author = "Alexandru Ghitza",
title = "Distinguishing {Hecke} Eigenforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1247--1253",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004708",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004708",
abstract = "We revisit a theorem of Ram Murty about the number of
initial Fourier coefficients that two cuspidal
eigenforms of different weights can have in common. We
prove an explicit upper bound on this number, and give
better conditional and unconditional asymptotic upper
bounds. Finally, we describe a numerical experiment
testing the sharpness of the upper bound in the case of
forms of level one.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Williams:2011:SFO,
author = "H. C. Williams and R. K. Guy",
title = "Some Fourth-Order Linear Divisibility Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1255--1277",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004587",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004587",
abstract = "We extend the Lucas--Lehmer theory for second-order
divisibility sequences to a large class of fourth-order
sequences, with appropriate laws of apparition and of
repetition. Examples are provided by the numbers of
perfect matchings, or of spanning trees, in families of
graphs, and by the numbers of points on elliptic curves
over finite fields. Whether there are fourth-order
divisibility sequences not covered by our theory is an
open question.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2011:GUN,
author = "Huaning Liu",
title = "{Gowers} Uniformity Norm and Pseudorandom Measures of
the Pseudorandom Binary Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1279--1302",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004137",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004137",
abstract = "Recently there has been much progress in the study of
arithmetic progressions. An important tool in these
developments is the Gowers uniformity norm. In this
paper we study the Gowers norm for pseudorandom binary
sequences, and establish some connections between these
two subjects. Some examples are given to show that the
``good'' pseudorandom sequences have small Gowers norm.
Furthermore, we introduce two large families of
pseudorandom binary sequences constructed by the
multiplicative inverse and additive character, and
study the pseudorandom measures and the Gowers norm of
these sequences by using the estimates of exponential
sums and properties of the Vandermonde determinant. Our
constructions are superior to the previous ones from
some points of view.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dahmen:2011:RMA,
author = "Sander R. Dahmen",
title = "A refined modular approach to the {Diophantine}
equation $ x^2 + y^{2 n} = z^3 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1303--1316",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004472",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004472",
abstract = "Let n be a positive integer and consider the
Diophantine equation of generalized Fermat type x$^2$ +
y$^{2n}$ = z$^3$ in nonzero coprime integer unknowns
x,y,z. Using methods of modular forms and Galois
representations for approaching Diophantine equations,
we show that for n \in {5,31} there are no solutions to
this equation. Combining this with previously known
results, this allows a complete description of all
solutions to the Diophantine equation above for n \leq
10$^7$. Finally, we show that there are also no
solutions for n \equiv -1 (mod 6).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2011:DTS,
author = "Zhixin Liu and Guangshi L{\"u}",
title = "Density of Two Squares of Primes and Powers of $2$",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1317--1329",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004605",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004605",
abstract = "As the generalization of the problem of Romanoff, we
establish that a positive proportion of integers can be
written as the sum of two squares of primes and two
powers of 2. We also prove that every large even
integer can be written as the sum of two primes and 12
powers of 2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baruah:2011:SCD,
author = "Nayandeep Deka Baruah and Kanan Kumari Ojah",
title = "Some Congruences Deducible from {Ramanujan}'s Cubic
Continued Fraction",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1331--1343",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004745",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004745",
abstract = "We present some interesting Ramanujan-type congruences
for some partition functions arising from Ramanujan's
cubic continued fraction. One of our results states
that if p$_3$ (n) is defined by, then p$_3$ (9n + 8)
\equiv 0 (mod 3$^4$).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Harada:2011:CSU,
author = "Masaaki Harada",
title = "Construction of Some Unimodular Lattices with Long
Shadows",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1345--1358",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004794",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004794",
abstract = "In this paper, we construct odd unimodular lattices in
dimensions n = 36,37 having minimum norm 3 and 4s = n -
16, where s is the minimum norm of the shadow. We also
construct odd unimodular lattices in dimensions n =
41,43,44 having minimum norm 4 and 4s = n - 24.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wang:2011:API,
author = "Xinna Wang and Yingchun Cai",
title = "An Additive Problem Involving {Piatetski--Shapiro}
Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1359--1378",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004630",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004630",
abstract = "Let P$_r$ denote an almost-prime with at most r prime
factors, counted according to multiplicity. In this
paper it is proved that there exist infinitely many
primes of the form p = [n$^c$ ] such that p + 2 =
P$_r$, where r is the least positive integer satisfying
certain inequalities. In particular for we have r = 5.
This result constitutes an improvement upon that of T.
P. Peneva.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Park:2011:ALG,
author = "Jeehoon Park",
title = "Another look at {Gross--Stark} units over the number
field {$ \mathbb {Q} $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1379--1393",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004150",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004150",
abstract = "We provide another description of the Gross--Stark
units over the rational field {$ \mathbb {Q} $}
(studied in [B. Gross, $p$-adic $L$-series at s = 0,
{\em J. Fac. Sci. Univ. Tokyo\/} 28(3) (1981)
979--994]) which is essentially a Gauss sum, using a
$p$-adic multiplicative integral of the {\em $p$-adic
Kubota--Leopoldt distribution\/}, and give a simplified
proof of the Ferrero--Greenberg theorem (see [B.
Ferrero and R. Greenberg, On the behavior of $p$-adic
{$L$}-functions at s = 0, {\em Invent. Math.\/} 50(1)
(1978/79) 91--102]) for $p$-adic Hurwitz zeta
functions. This is a precise analog for {$ \mathbb
{Q}$} of Darmon--Dasgupta's work on {\em elliptic units
for real quadratic fields\/} (see [H. Darmon and S.
Dasgupta, Elliptic units for real quadratic fields,
{\em Ann. of Math. (2)\/} 163(1) (2006) 301--346]).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ryan:2011:BTC,
author = "Nathan C. Ryan and Gonzalo Tornar{\'i}a",
title = "A {B{\"o}cherer}-type conjecture for paramodular
forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "5",
pages = "1395--1411",
month = aug,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004629",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004629",
abstract = "In the 1980s B{\"o}cherer formulated a conjecture
relating the central value of the quadratic twists of
the spinor {$L$}-function attached to a Siegel modular
form F to the coefficients of F. He proved the
conjecture when F is a Saito--Kurokawa lift. Later
Kohnen and Ku{\ss} gave numerical evidence for the
conjecture in the case when F is a rational eigenform
that is not a Saito--Kurokawa lift. In this paper we
develop a conjecture relating the central value of the
quadratic twists of the spinor {$L$}-function attached
to a paramodular form and the coefficients of the form.
We prove the conjecture in the case when the form is a
Gritsenko lift and provide numerical evidence when it
is not a lift.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Goldston:2011:JCG,
author = "D. A. Goldston and A. H. Ledoan",
title = "Jumping Champions and Gaps Between Consecutive
Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1413--1421",
month = sep,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S179304211100471X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100471X",
abstract = "The most common difference that occurs among the
consecutive primes less than or equal to x is called a
jumping champion. Occasionally there are ties.
Therefore there can be more than one jumping champion
for a given x. In 1999 Odlyzko, Rubinstein and Wolf
provided heuristic and empirical evidence in support of
the conjecture that the numbers greater than 1 that are
jumping champions are 4 and the primorials 2, 6, 30,
210, 2310,\ldots. As a step toward proving this
conjecture they introduced a second weaker conjecture
that any fixed prime p divides all sufficiently large
jumping champions. In this paper we extend a method of
Erd{\H{o}}s and Straus from 1980 to prove that the
second conjecture follows directly from the prime pair
conjecture of Hardy and Littlewood.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Djankovic:2011:NFA,
author = "Goran Djankovi{\'c}",
title = "Nonvanishing of the family of {$ \Gamma_1 (q)
$}-automorphic {$L$}-functions at the central point",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1423--1439",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004800",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004800",
abstract = "We investigate proportion of nonvanishing central
values L(f, 1/2) of {$L$}-functions associated to the
basis of holomorphic modular forms of fixed weight k
with respect to \Gamma$_1$ (q), in the limit when q
\rightarrow \infty along the primes. Motivation is a
contrast between \Gamma$_0$ (q) and \Gamma$_1$ (q)
families in the sense of underlying harmonic
analysis.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Komori:2011:FED,
author = "Yasushi Komori and Kohji Matsumoto and Hirofumi
Tsumura",
title = "Functional Equations for Double {$L$}-Functions and
Values at Non-Positive Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1441--1461",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004551",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004551",
abstract = "We consider double {$L$}-functions with periodic
coefficients and complex parameters. We prove
functional equations for them, which is of traditional
symmetric form on certain hyperplanes. These are
character analogs of our previous result on double
zeta-functions. We further evaluate double
{$L$}-functions at non-positive integers and construct
certain $p$-adic double {$L$}-functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gao:2011:QAN,
author = "Weidong Gao and Alfred Geroldinger and Qinghong Wang",
title = "A Quantitative Aspect of Non-Unique Factorizations:
the {Narkiewicz} Constants",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1463--1502",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004721",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004721",
abstract = "Let K be an algebraic number field with non-trivial
class group G and let be its ring of integers. For k
\in \mathbb{N} and some real x \geq 1, let F$_k$ (x)
denote the number of non-zero principal ideals with
norm bounded by x such that a has at most k distinct
factorizations into irreducible elements. It is well
known that F$_k$ (x) behaves, for x \rightarrow \infty,
asymptotically like x(log x)$^{-1 + 1 / |G|}$ (log log
x)$^{N k (G)}$. We study N$_k$ (G) with new methods
from Combinatorial Number Theory.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pitoun:2011:CCM,
author = "Fr{\'e}d{\'e}ric Pitoun",
title = "Conoyaux de capitulation et modules d'{Iwasawa}.
({French}) [{Capitulation} co-kernels and {Iwasawa}
modules]",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1503--1517",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004861",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004861",
abstract = "Soit F un corps de nombres totalement r{\'e}el et p un
premier impair, on note $ K_0 $ = F(\zeta$_p$). Pour n
\in \mathbb{N}, $ K_n$ d{\'e}signe le n-i{\`e}me
{\'e}tage de la {\mathbb{Z}}$_p$ extension cyclotomique
$ K_{\infty }$ /K$_0$, A$_n$ est la $p$-partie du
groupe des classes de $ K_n$, et N$_{\infty }$ est
l'extension de $ K_{\infty }$ obtenue en extrayant des
racines $p$-primaires d'unit{\'e}s. Le but de cet
article est de montrer que le dual de Pontryagin de la
partie plus des conoyaux de capitulation, sur laquelle
l'action de \Gamma a {\'e}t{\'e} tordue une fois par le
caract{\`e}re cyclotomique et la partie moins de la
{\mathbb{Z}}$_p$ torsion du groupe de Galois
Gal(N$_{\infty }$ \cap L$_{\infty }$ /K$_{\infty }$)
sont isomorphes. Let F be a totally real number field
and p an odd prime, we note $ K_0$ = F(\zeta$_p$). For
an integer n, $ K_n$ is the nth floor of the
{\mathbb{Z}}$_p$-cyclotomic extension $ K_{\infty }$
/K$_0$, A$_n$ is the $p$-part of the class group of $
K_n$, and N$_{\infty }$ is the extension of $ K_{\infty
}$ generated by $p$-primary roots of units. In this
article, we prove that the plus part of the
capitulation's cokernel, on which \Gamma -action was
twisted on time by the cyclotomic character, and the
minus part of the {\mathbb{Z}}$_p$-torsion of the
Galois group Gal(N$_{\infty }$ \cap L$_{\infty }$
/K$_{\infty }$) is isomorphic.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Blache:2011:NPC,
author = "R{\'e}gis Blache",
title = "{Newton} Polygons for Character Sums and
{Poincar{\'e}} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1519--1542",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004368",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004368",
abstract = "In this paper, we precise the asymptotic behavior of
Newton polygons of {$L$}-functions associated to
character sums, coming from certain n variable Laurent
polynomials. In order to do this, we use the free sum
on convex polytopes. This operation allows the
determination of the limit of generic Newton polygons
for the sum \Delta = \Delta$_1$ \oplus \Delta$_2$ when
we know the limit of generic Newton polygons for each
factor. To our knowledge, these are the first results
concerning the asymptotic behavior of Newton polygons
for multivariable polynomials when the generic Newton
polygon differs from the combinatorial (Hodge) polygon
associated to the polyhedron.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Girstmair:2011:CFJ,
author = "Kurt Girstmair",
title = "Continued Fractions and {Jacobi} Symbols",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1543--1555",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004848",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004848",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ostafe:2011:MCS,
author = "Alina Ostafe and Igor E. Shparlinski and Arne
Winterhof",
title = "Multiplicative Character Sums of a Class of Nonlinear
Recurrence Vector Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1557--1571",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004484",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004484",
abstract = "We estimate multiplicative character sums along the
orbits of a class of nonlinear recurrence vector
sequences. In the one-dimensional case, only much
weaker estimates are known and our results have no
one-dimensional analogs.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Papikian:2011:GAG,
author = "Mihran Papikian",
title = "On Generators of Arithmetic Groups Over Function
Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1573--1587",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004265",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004265",
abstract = "Let F = {$ \mathbb {F} $}$_q$ (T) be the field of
rational functions with {$ \mathbb {F}
$}$_q$-coefficients, and A = {$ \mathbb {F} $}$_q$ [T]
be the subring of polynomials. Let D be a division
quaternion algebra over F which is split at 1/T. For
certain A-orders in D we find explicit finite sets
generating their groups of units.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Xia:2011:DRG,
author = "Ernest X. W. Xia and X. M. Yao",
title = "The $8$-dissection of the
{Ramanujan--G{\"o}llnitz--Gordon} continued fraction by
an iterative method",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1589--1593",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004824",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004824",
abstract = "In this paper, we present an iterative method to
derive the 8-dissections of the
Ramanujan--G{\"o}llnitz--Gordon continued fraction and
its reciprocal which were first discovered by
Hirschhorn.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chen:2011:CP,
author = "Yong-Gao Chen and Jing-Rui Lou",
title = "The congruent properties for $ r_s(n) $",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1595--1602",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004885",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See erratum \cite{Chen:2013:ECP}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004885",
abstract = "Let r$_s$ (n) denote the number of ways to write an
integer n as the sum of s squares of integers. In this
paper, the congruent properties for r$_s$ (n) are
studied. We give the elementary combinatorial proofs of
all related results due to Wagstaff and Chen, and
obtain some new results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Oh:2011:RAP,
author = "Byeong-Kweon Oh",
title = "Representations of Arithmetic Progressions by Positive
Definite Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1603--1614",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004915",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004915",
abstract = "For a positive integer d and a non-negative integer a,
let S$_{d, a}$ be the set of all integers of the form
dn + a for any non-negative integer n. A (positive
definite integral) quadratic form f is said to be
S$_{d, a}$- {\em universal\/} if it represents all
integers in the set S$_{d, a}$, and is said to be
S$_{d, a}$- {\em regular\/} if it represents all
integers in the non-empty set S$_{d, a}$ \cap Q((f)),
where Q(gen(f)) is the set of all integers that are
represented by the genus of f. In this paper, we prove
that there is a polynomial U(x,y) \in {$ \mathbb
{Q}$}[x,y] (R(x,y) \in {$ \mathbb {Q}$}[x,y]) such that
the discriminant df for any S$_{d, a}$ universal
(S$_{d, a}$-regular) ternary quadratic forms is bounded
by U(d,a) (respectively, R(d,a)).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Xiong:2011:TII,
author = "Xinhua Xiong",
title = "Two Identities Involving the Cubic Partition
Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1615--1626",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004757",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004757",
abstract = "We give a very elementary proof of an identity
involving the cubic partition function and we also give
an elementary proof of a new identity for the cubic
partition function which is analogs to Zuckerman's
identity for the ordinary partition function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fukuda:2011:WCN,
author = "Takashi Fukuda and Keiichi Komatsu",
title = "{Weber}'s class number problem in the cyclotomic {$
\mathbb {Z}_2 $}-extension of {$ \mathbb {Q} $},
{III}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1627--1635",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004782",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004782",
abstract = "Let h$_n$ denote the class number of which is a cyclic
extension of degree 2$^n$ over the rational number
field {$ \mathbb {Q}$}. There are no known examples of
h$_n$ > 1. We prove that a prime number \ell does not
divide h$_n$ for all n \geq 1 if \ell is less than
10$^9$ or \ell satisfies a congruence relation \ell
\nequiv \pm 1 (mod 32).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sakai:2011:AOP,
author = "Yuichi Sakai",
title = "The {Atkin} Orthogonal Polynomials for the Low-Level
{Fricke} Groups and Their Application",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1637--1661",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004460",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004460",
abstract = "Kaneko and Zagier proved the relation between the
Atkin orthogonal polynomials and supersingular
j-polynomials for PSL$_2$ ({\mathbb{Z}}). Tsutsumi also
proved its relation for the Hecke subgroups of level
less than or equal to 4. In this paper, we define the
Atkin inner product for the Fricke groups of level less
than or equal to 3 and construct the Atkin orthogonal
polynomials. Then, we give the relation between
supersingular -polynomials defined by Koike and its
polynomials. We also give extremal quasimodular forms
of depth 1 by using its orthogonal polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Turkelli:2011:CMC,
author = "Seyfi T{\"u}rkelli",
title = "Counting multisections in conic bundles over a curve
defined over {$ \mathbb {F}_q $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1663--1680",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100485X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100485X",
abstract = "For a given conic bundle X over a curve C defined over
{$ \mathbb {F} $}$_q$, we count irreducible branch
covers of C in X of degree d and height e \gg 1. As a
special case, we get the number of algebraic numbers of
degree d and height e over the function field {$
\mathbb {F} $}$_q$ (C).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hong:2011:ABS,
author = "Shaofang Hong and Raphael Loewy",
title = "Asymptotic behavior of the smallest eigenvalue of
matrices associated with completely even functions $
(\bmod r) $",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "6",
pages = "1681--1704",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100437X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100437X",
abstract = "In this paper, we present systematically analysis on
the smallest eigenvalue of matrices associated with
completely even functions (mod r). We obtain several
theorems on the asymptotic behavior of the smallest
eigenvalue of matrices associated with completely even
functions (mod r). In particular, we get information on
the asymptotic behavior of the smallest eigenvalue of
the famous Smith matrices. Finally some examples are
given to demonstrate the main results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knopfmacher:2011:PPN,
author = "Arnold Knopfmacher and Florian Luca",
title = "On Prime-Perfect Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1705--1716",
month = nov,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111004447",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004447",
abstract = "We prove that the Diophantine equation has only
finitely many positive integer solutions k, p$_1$,
\ldots, p$_k$, r$_1$, \ldots, r$_k$, where p$_1$,
\ldots, p$_k$ are distinct primes. If a positive
integer n has prime factorization, then represents the
number of ordered factorizations of n into prime parts.
Hence, solutions to the above Diophantine equation are
designated as prime-perfect numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ballot:2011:MD,
author = "Christian Ballot and Mireille Car",
title = "On {Murata} Densities",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1717--1736",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100440X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100440X",
abstract = "In this paper, we set up an abstract theory of Murata
densities, well tailored to general arithmetical
semigroups. In [On certain densities of sets of primes,
{\em Proc. Japan Acad. Ser. A Math. Sci.\/} 56(7)
(1980) 351--353; On some fundamental relations among
certain asymptotic densities, {\em Math. Rep. Toyama
Univ.\/} 4(2) (1981) 47--61], Murata classified certain
prime density functions in the case of the arithmetical
semigroup of natural numbers. Here, it is shown that
the same density functions will obey a very similar
classification in any arithmetical semigroup whose
sequence of norms satisfies certain general growth
conditions. In particular, this classification holds
for the set of monic polynomials in one indeterminate
over a finite field, or for the set of ideals of the
ring of S-integers of a global function field (S
finite).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hare:2011:SD,
author = "Kevin G. Hare and Shanta Laishram and Thomas Stoll",
title = "The sum of digits of $n$ and $ n^2$",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1737--1752",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004319",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004319",
abstract = "Let s$_q$ (n) denote the sum of the digits in the
q-ary expansion of an integer n. In 2005, Melfi
examined the structure of n such that s$_2$ (n) = s$_2$
(n$^2$). We extend this study to the more general case
of generic q and polynomials p(n), and obtain, in
particular, a refinement of Melfi's result. We also
give a more detailed analysis of the special case p(n)
= n$^2$, looking at the subsets of n where s$_q$ (n) =
s$_q$ (n$^2$) = k for fixed k.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bazzanella:2011:TCR,
author = "Danilo Bazzanella",
title = "Two Conditional Results About Primes in Short
Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1753--1759",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004563",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004563",
abstract = "In 1937, Ingham proved that \psi (x + x$^{\theta }$) -
\psi (x) \sim x$^{\theta }$ for x \rightarrow \infty,
under the assumption of the Lindel{\"o}f hypothesis for
\theta > 1/2. In this paper we examine how the above
asymptotic formula holds by assuming in turn two
different heuristic hypotheses. It must be stressed
that both the hypotheses are implied by the
Lindel{\"o}f hypothesis.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ribenboim:2011:MPT,
author = "Paulo Ribenboim",
title = "Multiple patterns of $k$-tuples of integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1761--1779",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004733",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004733",
abstract = "The first proposition and its corollary are a
transfiguration of Dirichlet's pigeon-hole principle.
They are applied to show that a wide variety of
sequences display arbitrarily large patterns of sums,
differences, higher differences, etc. Among these, we
include sequences of primes in arithmetic progressions,
of powerful integers, sequences of integers with
radical index having a prescribed lower bound, and many
others. We also deal with patterns in iterated
sequences of primes, patterns of gaps between primes,
patterns of values of Euler's \phi -function, or their
gaps, as well as patterns related to the sequence of
Carmichael numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Faber:2011:NRI,
author = "Xander Faber and Benjamin Hutz and Michael Stoll",
title = "On the Number of Rational Iterated Preimages of the
Origin Under Quadratic Dynamical Systems",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1781--1806",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004162",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004162",
abstract = "For a quadratic endomorphism of the affine line
defined over the rationals, we consider the problem of
bounding the number of rational points that eventually
land at the origin after iteration. In the article
``Uniform bounds on pre-images under quadratic
dynamical systems,'' by two of the present authors and
five others, it was shown that the number of rational
iterated preimages of the origin is bounded as one
varies the morphism in a certain one-dimensional
family. Subject to the validity of the Birch and
Swinnerton-Dyer conjecture and some other related
conjectures for the $L$-series of a specific abelian
variety and using a number of modern tools for locating
rational points on high genus curves, we show that the
maximum number of rational iterated preimages is six.
We also provide further insight into the geometry of
the ``preimage curves.''",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chambert-Loir:2011:TJS,
author = "Antoine Chambert-Loir",
title = "The Theorem of {Jentzsch--Szeg{\H{o}}} on an Analytic
Curve: Application to the Irreducibility of Truncations
of Power Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1807--1823",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004691",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004691",
abstract = "A theorem of Jentzsch--Szeg{\H{o}} describes the limit
measure of a sequence of discrete measures associated
to zeroes of a sequence of polynomials in one variable.
Following the presentation by Andrievskii and Blatt in
[ {\em Discrepancy of Signed Measures and Polynomial
Approximation\/}, Springer Monographs in Mathematics
(Springer-Verlag, New York, 2002)] we extend this
theorem to compact Riemann surfaces and to analytic
curves in the sense of Berkovich over ultrametric
fields, using classical potential theory in the former
case, and Baker/Rumely, Thuillier's potential theory on
analytic curves in the latter case. We then apply this
equidistribution theorem to the question of
irreducibility of truncations of power series with
coefficients in ultrametric fields. {\em R{\'e}sum{\'e}
fran{\c{c}}ais\/}: Le th{\'e}or{\`e}me de
Jentzsch--Szeg{\H{o}} d{\'e}crit la mesure limite d'une
suite de mesures discr{\`e}tes associ{\'e}e aux
z{\'e}ros d'une suite convenable de polyn{\^o}mes en
une variable. Suivant la pr{\'e}sentation que font
Andrievskii et Blatt dans [ {\em Discrepancy of Signed
Measures and Polynomial Approximation\/}, Springer
Monographs in Mathematics (Springer-Verlag, New York,
2002)] on {\'e}tend ici ce r{\'e}sultat aux surfaces de
Riemann compactes, puis aux courbes analytiques sur un
corps ultram{\'e}trique. On donne pour finir quelques
corollaires du cas particulier de la droite projective
sur un corps ultram{\'e}trique {\`a}
l'irr{\'e}ductibilit{\'e} des polyn{\^o}mes-sections
d'une s{\'e}rie enti{\`e}re en une variable.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Berger:2011:AFD,
author = "Laurent Berger",
title = "A $p$-adic family of dihedral {$ (\phi,
\Gamma)$}-modules",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1825--1834",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004770",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004770",
abstract = "The goal of this paper is to construct explicitly a
$p$-adic family of representations (which are dihedral
representations), to construct their attached (\phi,
\Gamma)-modules by writing down explicit matrices for
\phi and for the action of \Gamma, and finally to
determine which of these are trianguline.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zumalacarregui:2011:CPM,
author = "Ana Zumalac{\'a}rregui",
title = "Concentration of Points on Modular Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1835--1839",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004897",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004897",
abstract = "Let Q(x, y) be a quadratic form with discriminant D
\neq 0. We obtain non-trivial upper bound estimates for
the number of solutions of the congruence Q(x, y)
\equiv \lambda (mod p), where p is a prime and x, y lie
in certain intervals of length M, under the assumption
that Q(x, y) - \lambda is an absolutely irreducible
polynomial modulo p. In particular, we prove that the
number of solutions to this congruence is M$^{o(1)}$
when M \ll p$^{1 / 4}$. These estimates generalize a
previous result by Cilleruelo and Garaev on the
particular congruence xy \equiv \lambda (mod p).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Petersen:2011:EAN,
author = "Kathleen L. Petersen and Christopher D. Sinclair",
title = "Equidistribution of Algebraic Numbers of Norm One in
Quadratic Number Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1841--1861",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004666",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004666",
abstract = "Given a fixed quadratic extension K of {$ \mathbb {Q}
$}, we consider the distribution of elements in K of
norm one (denoted ). When K is an imaginary quadratic
extension, is naturally embedded in the unit circle in
{\mathbb{C}} and we show that it is equidistributed
with respect to inclusion as ordered by the absolute
Weil height. By Hilbert's Theorem 90, an element in can
be written as for some, which yields another ordering
of given by the minimal norm of the associated
algebraic integers. When K is imaginary we also show
that is equidistributed in the unit circle under this
norm ordering. When K is a real quadratic extension, we
show that is equidistributed with respect to norm,
under the map \beta \mapsto log|\beta |(mod
log|\epsilon$^2$ |) where \epsilon is a fundamental
unit of.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Reznick:2011:STC,
author = "Bruce Reznick and Jeremy Rouse",
title = "On the Sums of Two Cubes",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1863--1882",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004903",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004903",
abstract = "We solve the equation f(x, y)$^3$ + g(x, y)$^3$ =
x$^3$ + y$^3$ for homogeneous f, g \in {\mathbb{C}}(x,
y), completing an investigation begun by Vi{\`e}te in
1591. The usual addition law for elliptic curves and
composition give rise to two binary operations on the
set of solutions. We show that a particular subset of
the set of solutions is ring isomorphic to
{\mathbb{Z}}[e$^{2 \pi i / 3}$ ].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bouganis:2011:NAC,
author = "Thanasis Bouganis",
title = "Non--{Abelian} Congruences Between Special Values of
{$L$}-Functions of Elliptic Curves: the {CM} Case",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1883--1934",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100468X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100468X",
abstract = "In this work we prove congruences between special
values of {$L$}-functions of elliptic curves with CM
that seem to play a central role in the analytic side
of the non-commutative Iwasawa theory. These
congruences are the analog for elliptic curves with CM
of those proved by Kato, Ritter and Weiss for the Tate
motive. The proof is based on the fact that the
critical values of elliptic curves with CM, or what
amounts to the same, the critical values of
Gr{\"o}ssencharacters, can be expressed as values of
Hilbert--Eisenstein series at CM points. We believe
that our strategy can be generalized to provide
congruences for a large class of $L$-values.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Li:2011:DCU,
author = "Yan Li and Lianrong Ma",
title = "Double Coverings and Unit Square Problems for
Cyclotomic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1935--1944",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004836",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004836",
abstract = "In this paper, using the theory of double coverings of
cyclotomic fields, we give a formula for, where K = {$
\mathbb {Q} $}(\zeta$_n$), G = Gal(K/{$ \mathbb {Q}$}),
{$ \mathbb {F} $}$_2$ = {\mathbb{Z}}/2{\mathbb{Z}} and
U$_K$ is the unit group of K. We explicitly determine
all the cyclotomic fields K = {$ \mathbb
{Q}$}(\zeta$_n$) such that . Then we apply it to the
unit square problem raised in [Y. Li and X. Zhang,
Global unit squares and local unit squares, {\em J.
Number Theory\/} 128 (2008) 2687--2694]. In particular,
we prove that the unit square problem does not hold for
{$ \mathbb {Q}$}(\zeta$_n$) if n has more than three
distinct prime factors, i.e. for each odd prime p,
there exists a unit, which is a square in all local
fields {$ \mathbb {Q}$}(\zeta$_n$)$_v$ with v | p but
not a square in {$ \mathbb {Q}$}(\zeta$_n$), if n has
more than three distinct prime factors.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Huber:2011:DEC,
author = "Tim Huber",
title = "Differential Equations for Cubic Theta Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1945--1957",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004873",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004873",
abstract = "We show that the cubic theta functions satisfy two
distinct coupled systems of nonlinear differential
equations. The resulting relations are analogous to
Ramanujan's differential equations for Eisenstein
series on the full modular group. We deduce the cubic
analogs presented here from trigonometric series
identities arising in Ramanujan's original paper on
Eisenstein series. Several consequences of these
differential equations are established, including a
short proof of a famous cubic theta function identity
derived by J. M. Borwein and P. B. Borwein.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Guo:2011:FSA,
author = "Victor J. W. Guo and Jiang Zeng",
title = "Factors of Sums and Alternating Sums Involving
Binomial Coefficients and Powers of Integers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "7",
pages = "1959--1976",
month = nov,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004812",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:26 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004812",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Merila:2011:NLC,
author = "Ville Meril{\"a}",
title = "A Nonvanishing Lemma for Certain {Pad{\'e}}
Approximations of the Second Kind",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "1977--1997",
month = dec,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042111004964",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004964",
abstract = "We prove the nonvanishing lemma for explicit second
kind Pad{\'e} approximations to generalized
hypergeometric and q-hypergeometric functions. The
proof is based on an evaluation of a generalized
Vandermonde determinant. Also, some immediate
applications to the Diophantine approximation is given
in the form of sharp linear independence measures for
hypergeometric E- and G-functions in algebraic number
fields with different valuations.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Nathanson:2011:PAN,
author = "Melvyn B. Nathanson",
title = "Problems in additive number theory, {IV}: Nets in
groups and shortest length $g$-adic representations",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "1999--2017",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004940",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004940",
abstract = "The number theoretic analog of a net in metric
geometry suggests new problems and results in
combinatorial and additive number theory. For example,
for a fixed integer $ g \geq 2 $, the study of $h$-nets
in the additive group of integers with respect to the
generating set $ A_g = \{ 0 \} \cup \{ \pm g^i \colon i
= 0, 1, 2, \ldots \} $ requires a knowledge of the word
lengths of integers with respect to $ A_g$. A $g$-adic
representation of an integer is described that
algorithmically produces a representation of shortest
length. Additive complements and additive asymptotic
complements are also discussed, together with their
associated minimality problems.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Haessig:2011:FSP,
author = "C. Douglas Haessig and Antonio Rojas-Le{\'o}n",
title = "{$L$}-Functions of Symmetric Powers of the Generalized
{Airy} Family of Exponential Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2019--2064",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005040",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005040",
abstract = "This paper looks at the {$L$}-function of the kth
symmetric power of the -sheaf Ai$_f$ over the affine
line associated to the generalized Airy family of
exponential sums. Using \ell -adic techniques, we
compute the degree of this rational function as well as
the local factors at infinity. Using $p$-adic
techniques, we study the $q$-adic Newton polygon of the
{$L$}-function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pande:2011:DGR,
author = "Aftab Pande",
title = "Deformations of {Galois} Representations and the
Theorems of {Sato--Tate} and {Lang--Trotter}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2065--2079",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004939",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004939",
abstract = "We construct infinitely ramified Galois
representations \rho such that the a$_l$ (\rho)'s have
distributions in contrast to the statements of
Sato--Tate, Lang--Trotter and others. Using similar
methods we deform a residual Galois representation for
number fields and obtain an infinitely ramified
representation with very large image, generalizing a
result of Ramakrishna.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bremner:2011:X,
author = "Andrew Bremner and Maciej Ulas",
title = "On $ x^a \pm y^b \pm z^c \pm w^d = 0 $, $ 1 / a + 1 /
b + 1 / c + 1 / d = 1 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2081--2090",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005076",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005076",
abstract = "It is well known that the Diophantine equations x$^4$
+ y$^4$ = z$^4$ + w$^4$ and x$^4$ + y$^4$ + z$^4$ =
w$^4$ each have infinitely many rational solutions. It
is also known for the equation x$^6$ + y$^6$- z$^6$ =
w$^2$. We extend the investigation to equations x$^a$
\pm y$^b$ = \pm z$^c$ \pm w$^d$, a, b, c, d \in Z, with
1/a + 1/b + 1/c + 1/d = 1. We show, with one possible
exception, that if there is a solution of the equation
in the reals, then the equation has infinitely many
solutions in the integers. Of particular interest is
the equation x$^6$ + y$^6$ + z$^6$ = w$^2$ because of
its classical nature; but there seem to be no
references in the literature.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Yu:2011:EMO,
author = "Chia-Fu Yu",
title = "On the Existence of Maximal Orders",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2091--2114",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005003",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005003",
abstract = "We generalize the existence of maximal orders in a
semi-simple algebra for general ground rings. We also
improve several statements in Chaps. 5 and 6 of
Reiner's book [ {\em Maximal Orders\/}, London
Mathematical Society Monographs, Vol. 5 (Academic
Press, London, 1975), 395 pp.] concerning separable
algebras by removing the separability condition,
provided the ground ring is only assumed to be
Japanese, a very mild condition. Finally, we show the
existence of maximal orders as endomorphism rings of
abelian varieties in each isogeny class.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Qi:2011:MTS,
author = "Zhi Qi and Chang Yang",
title = "{Morita}'s Theory for the Symplectic Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2115--2137",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004952",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004952",
abstract = "We construct and study the holomorphic discrete series
representations and the principal series
representations of the symplectic group Sp(2n, F) over
a $p$-adic field F as well as a duality between some
sub-representations of these two representations. The
constructions of these two representations generalize
those defined in Morita and Murase's works. Moreover,
Morita built a duality for SL(2, F) defined by
residues. We view the duality we defined as an
algebraic interpretation of Morita's duality in some
extent and its generalization to the symplectic
groups.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lebacque:2011:LDZ,
author = "Philippe Lebacque and Alexey Zykin",
title = "On Logarithmic Derivatives of Zeta Functions in
Families of Global Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2139--2156",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005015",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005015",
abstract = "We prove a formula for the limit of logarithmic
derivatives of zeta functions in families of global
fields with an explicit error term. This can be
regarded as a rather far reaching generalization of the
explicit Brauer--Siegel theorem both for number fields
and function fields.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Habsieger:2011:SCP,
author = "Laurent Habsieger and Emmanuel Royer",
title = "Spiegelungssatz: a Combinatorial Proof for the
$4$-Rank",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2157--2170",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005106",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005106",
abstract = "The Spiegelungssatz is an inequality between the
4-ranks of the narrow ideal class groups of the
quadratic fields and . We provide a combinatorial proof
of this inequality. Our interpretation gives an affine
system of equations that allows to describe precisely
some equality cases.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Vega:2011:HFF,
author = "M. Valentina Vega",
title = "Hypergeometric Functions Over Finite Fields and Their
Relations to Algebraic Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2171--2195",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004976",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004976",
abstract = "In this work we present an explicit relation between
the number of points on a family of algebraic curves
over {$ \mathbb {F} $}$_q$ and sums of values of
certain hypergeometric functions over {$ \mathbb {F}
$}$_q$. Moreover, we show that these hypergeometric
functions can be explicitly related to the roots of the
zeta function of the curve over {$ \mathbb {F} $}$_q$
in some particular cases. A general conjecture relating
these last two is presented and advances toward its
proof are shown in the last section.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jabuka:2011:WTD,
author = "Stanislav Jabuka and Sinai Robins and Xinli Wang",
title = "When Are Two {Dedekind} Sums Equal?",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2197--2202",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005088",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005088",
abstract = "A natural question about Dedekind sums is to find
conditions on the integers a$_1$, a$_2$, and b such
that s(a$_1$, b) = s(a$_2$, b). We prove that if the
former equality holds then b|(a$_1$ a$_2$- 1)(a$_1$-
a$_2$). Surprisingly, to the best of our knowledge such
statements have not appeared in the literature. A
similar theorem is proved for the more general
Dedekind--Rademacher sums as well, namely that for any
fixed non-negative integer n, a positive integer
modulus b, and two integers a$_1$ and a$_2$ that are
relatively prime to b, the hypothesis r$_n$ (a$_1$, b)
= r$_n$ (a$_2$, b) implies that b|(6n$^2$ + 1 - a$_1$
a$_2$)(a$_2$- a$_1$).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Smith:2011:VBD,
author = "Ethan Smith",
title = "A Variant of the {Barban--Davenport--Halberstam
Theorem}",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2203--2218",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100499X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100499X",
abstract = "Let L/K be a Galois extension of number fields. The
problem of counting the number of prime ideals {$
\mathfrak {p} $} of K with fixed Frobenius class in
Gal(L/K) and norm satisfying a congruence condition is
considered. We show that the square of the error term
arising from the Chebotar{\"e}v Density Theorem for
this problem is small ``on average''. The result may be
viewed as a variation on the classical
Barban--Davenport--Halberstam Theorem.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Harvey:2011:CDI,
author = "M. P. Harvey",
title = "Cubic {Diophantine} Inequalities Involving a Norm
Form",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2219--2235",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005052",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005052",
abstract = "We apply Freeman's variant of the Davenport--Heilbronn
method to provide an asymptotic formula for the number
of small values taken by a certain family of cubic
forms with real coefficients. The cubic forms in
question arise as the sum of a diagonal form and a norm
form and should have at least seven variables.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rolen:2011:GCN,
author = "Larry Rolen",
title = "A Generalization of the Congruent Number Problem",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2237--2247",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005039",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005039",
abstract = "We study a certain generalization of the classical
Congruent Number Problem. Specifically, we study
integer areas of rational triangles with an arbitrary
fixed angle \theta. These numbers are called \theta
-congruent. We give an elliptic curve criterion for
determining whether a given integer n is \theta
congruent. We then consider the ``density'' of integers
n which are \theta -congruent, as well as the related
problem giving the ``density'' of angles \theta for
which a fixed n is congruent. Assuming the
Shafarevich--Tate conjecture, we prove that both
proportions are at least 50\% in the limit. To obtain
our result we use the recently proven $p$-parity
conjecture due to Monsky and the Dokchitsers as well as
a theorem of Helfgott on average root numbers in
algebraic families.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Radu:2011:CPM,
author = "Silviu Radu and James A. Sellers",
title = "Congruence properties modulo $5$ and $7$ for the {$
\mathrm {pod}$} function",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2249--2259",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005064",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005064",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{ElBachraoui:2011:IFS,
author = "Mohamed {El Bachraoui}",
title = "Inductive Formulas for Some Arithmetic Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2261--2268",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S179304211100509X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211100509X",
abstract = "We prove recursive formulas involving sums of divisors
and sums of triangular numbers and give a variety of
identities relating arithmetic functions to divisor
functions providing inductive identities for such
arithmetic functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Graves:2011:NPE,
author = "Hester Graves",
title = "Has a Non-Principal {Euclidean} Ideal",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2269--2271",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111004988",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111004988",
abstract = "This paper introduces a totally real quartic number
field with a non-principal Euclidean ideal.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kim:2011:AVM,
author = "Min-Soo Kim and Su Hu",
title = "A $p$-adic view of multiple sums of powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2273--2288",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005027",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005027",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2011:AIV,
author = "Anonymous",
title = "Author Index (Volume 7)",
journal = j-INT-J-NUMBER-THEORY,
volume = "7",
number = "8",
pages = "2289--2295",
month = dec,
year = "2011",
DOI = "https://doi.org/10.1142/S1793042111005118",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042111005118",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{FreixasIMontplet:2012:JLC,
author = "Gerard {Freixas I.Montplet}",
title = "The {Jacquet--Langlands} Correspondence and the
Arithmetic {Riemann--Roch} Theorem for Pointed Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "1--29",
month = feb,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500017",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500017",
abstract = "We show how the Jacquet--Langlands correspondence and
the arithmetic Riemann--Roch theorem for pointed
curves, relate the arithmetic self-intersection numbers
of the sheaves of modular forms with their Petersson
norms --- on modular and Shimura curves: these are
equal modulo $ \sum_{l \in S} $ {$ \mathbb {Q} $} log
l, where S is a controlled set of primes. These
quantities were previously considered by Bost and
K{\"u}hn (modular curve case) and Kudla--Rapoport--Yang
and Maillot--Roessler (Shimura curve case). By the work
of Maillot and Roessler, our result settles a question
raised by Soul{\'e}.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Finotti:2012:NPC,
author = "Lu{\'i}s R. A. Finotti",
title = "Nonexistence of Pseudo-Canonical Liftings",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "31--51",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500029",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500029",
abstract = "In this paper we show that pseudo-canonical liftings
do not exist, by showing that if j$_0$ \mapsto (j$_0$,
J$_1$ (j$_0$), J$_2$ (j$_0$),\ldots) is the map that
gives canonical liftings for ordinary j$_0$, then J$_2$
has a pole at j$_0$ = 1728 if p \equiv 3 (mod 4) and
J$_3$ has a pole at j$_0$ = 0 if p \equiv 5 (mod 6).
Moreover, precise descriptions of J$_2$ and J$_3$ are
given.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Akbary:2012:GVT,
author = "Amir Akbary and Dragos Ghioca",
title = "A Geometric Variant of {Titchmarsh} Divisor Problem",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "53--69",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500030",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500030",
abstract = "We formulate a geometric analog of the Titchmarsh
divisor problem in the context of abelian varieties.
For any abelian variety A defined over {$ \mathbb {Q}
$}, we study the asymptotic distribution of the primes
of {\mathbb{Z}} which split completely in the division
fields of A. For all abelian varieties which contain an
elliptic curve we establish an asymptotic formula for
such primes under the assumption of Generalized Riemann
Hypothesis. We explain how to derive an unconditional
asymptotic formula in the case that the abelian variety
is a complex multiplication elliptic curve.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Amdeberhan:2012:II,
author = "Tewodros Amdeberhan and Christoph Koutschan and Victor
H. Moll and Eric S. Rowland",
title = "The iterated integrals of $ \ln (1 + x^n) $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "71--94",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500042",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500042",
abstract = "For a polynomial P, we consider the sequence of
iterated integrals of ln P(x). This sequence is
expressed in terms of the zeros of P(x). In the special
case of ln(1 + x$^2$), arithmetic properties of certain
coefficients arising are described. Similar
observations are made for ln(1 + x$^3$).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Castillo:2012:HOS,
author = "Daniel Macias Castillo",
title = "On higher-order {Stickelberger}-type theorems for
multi-quadratic extensions",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "95--110",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500054",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500054",
abstract = "We prove, for all quadratic and a wide range of
multi-quadratic extensions of global fields, a result
concerning the annihilation as Galois modules of ideal
class groups by explicit elements constructed from the
values of higher-order derivatives of Dirichlet
{$L$}-functions. This result simultaneously refines
Rubin's integral version of Stark's Conjecture and
provides evidence for the relevant case of the
Equivariant Tamagawa Number Conjecture of Burns and
Flach.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2012:TCA,
author = "Song Heng Chan and Renrong Mao",
title = "Two Congruences for {Appell--Lerch} Sums",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "111--123",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500066",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500066",
abstract = "Two congruences are proved for an infinite family of
Appell--Lerch sums. As corollaries, special cases imply
congruences for some of the mock theta functions of
order two, six and eight.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kadiri:2012:EZF,
author = "Habiba Kadiri",
title = "Explicit Zero-Free Regions for {Dedekind} Zeta
Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "125--147",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500078",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500078",
abstract = "Let K be a number field, n$_K$ be its degree, and
d$_K$ be the absolute value of its discriminant. We
prove that, if d$_K$ is sufficiently large, then the
Dedekind zeta function \zeta$_K$ (s) has no zeros in
the region:, , where log M = 12.55 log d$_K$ +
9.69n$_K$ log|\Im {$ \mathfrak {m} $} s| + 3.03 n$_K$ +
58.63. Moreover, it has at most one zero in the
region:, . This zero if it exists is simple and is
real. This argument also improves a result of Stark by
a factor of 2: \zeta$_K$ (s) has at most one zero in
the region, .",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Schweiger:2012:DAR,
author = "F. Schweiger",
title = "A $2$-Dimensional Algorithm Related to the
{Farey--Brocot} Sequence",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "149--160",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250008X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250008X",
abstract = "Moshchevitin and Vielhaber gave an interesting
generalization of the Farey--Brocot sequence for
dimension d \geq 2 (see [N. Moshchevitin and M.
Vielhaber, Moments for generalized Farey--Brocot
partitions, {\em Funct. Approx. Comment. Math.\/} 38
(2008), part 2, 131--157]). For dimension d = 2 they
investigate two special cases called algorithm and
algorithm. Algorithm is related to a proposal of
M{\"o}nkemeyer and to Selmer algorithm (see [G. Panti,
Multidimensional continued fractions and a Minkowski
function, {\em Monatsh. Math.\/} 154 (2008) 247--264]).
However, algorithm seems to be related to a new type of
2-dimensional continued fractions. The content of this
paper is first to describe such an algorithm and to
give some of its ergodic properties. In the second part
the dual algorithm is considered which behaves similar
to the Parry--Daniels map.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Filaseta:2012:S,
author = "M. Filaseta and S. Laishram and N. Saradha",
title = "Solving $ n (n + d) \cdots (n + (k - 1) d) = b y^2 $
with {$ P(b) \leq C k $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "161--173",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500091",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500091",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Noble:2012:AWD,
author = "Rob Noble",
title = "Asymptotics of the Weighted {Delannoy} Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "175--188",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500108",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500108",
abstract = "The weighted Delannoy numbers give a weighted count of
lattice paths starting at the origin and using only
minimal east, north and northeast steps. Full
asymptotic expansions exist for various diagonals of
the weighted Delannoy numbers. In the particular case
of the central weighted Delannoy numbers, certain
weights give rise to asymptotic coefficients that lie
in a number field. In this paper we apply a
generalization of a method of Stoll and Haible to
obtain divisibility properties for the asymptotic
coefficients in this case. We also provide a similar
result for a special case of the diagonal with slope
2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fukshansky:2012:WRI,
author = "Lenny Fukshansky and Kathleen Petersen",
title = "On Well-Rounded Ideal Lattices",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "189--206",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250011X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250011X",
abstract = "We investigate a connection between two important
classes of Euclidean lattices: well-rounded and ideal
lattices. A lattice of full rank in a Euclidean space
is called well-rounded if its set of minimal vectors
spans the whole space. We consider lattices coming from
full rings of integers in number fields, proving that
only cyclotomic fields give rise to well-rounded
lattices. We further study the well-rounded lattices
coming from ideals in quadratic rings of integers,
showing that there exist infinitely many real and
imaginary quadratic number fields containing ideals
which give rise to well-rounded lattices in the
plane.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sun:2012:ICN,
author = "Zhi-Hong Sun",
title = "Identities and Congruences for a New Sequence",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "207--225",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500121",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500121",
abstract = "Let [x] be the greatest integer not exceeding x. In
the paper we introduce the sequence {U$_n$ } given by
U$_0$ = 1 and, and establish many recursive formulas
and congruences involving {U$_n$ }.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{McGown:2012:NEC,
author = "Kevin J. McGown",
title = "Norm-{Euclidean} Cyclic Fields of Prime Degree",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "227--254",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500133",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500133",
abstract = "Let K be a cyclic number field of prime degree \ell .
Heilbronn showed that for a given \ell there are only
finitely many such fields that are norm-Euclidean. In
the case of \ell = 2 all such norm-Euclidean fields
have been identified, but for \ell \neq 2, little else
is known. We give the first upper bounds on the
discriminants of such fields when \ell > 2. Our methods
lead to a simple algorithm which allows one to generate
a list of candidate norm-Euclidean fields up to a given
discriminant, and we provide some computational
results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Perucca:2012:MSP,
author = "Antonella Perucca",
title = "The Multilinear Support Problem for Products of
{Abelian} Varieties and Tori",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "255--264",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500145",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500145",
abstract = "Let G be the product of an abelian variety and a torus
defined over a number field K. The aim of this paper is
detecting the dependence among some given rational
points of G by studying their reductions modulo all
primes of K. We show that if some simple conditions on
the order of the reductions of the points are satisfied
then there must be a dependency relation over the ring
of K-endomorphisms of G. We generalize Larsen's result
on the support problem to several points on products of
abelian varieties and tori.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Konstantinou:2012:RID,
author = "Elisavet Konstantinou and Aristides Kontogeorgis",
title = "{Ramanujan} invariants for discriminants congruent to
$ 5 (\bmod 24) $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "1",
pages = "265--287",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500157",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500157",
abstract = "In this paper we compute the minimal polynomials of
Ramanujan values for discriminants D \equiv 5 (mod 24).
Our method is based on Shimura Reciprocity Law as which
was made computationally explicit by Gee and
Stevenhagen in [Generating class fields using Shimura
reciprocity, in {\em Algorithmic Number Theory\/},
Lecture Notes in Computer Science, Vol. 1423 (Springer,
Berlin, 1998), pp. 441--453; MR MR1726092
(2000m:11112)]. However, since these Ramanujan values
are not class invariants, we present a modification of
the method used in [Generating class fields using
Shimura reciprocity, in {\em Algorithmic Number
Theory\/}, Lecture Notes in Computer Science, Vol. 1423
(Springer, Berlin, 1998), pp. 441--453; MR MR1726092
(2000m:11112)] which can be applied on modular
functions that do not necessarily yield class
invariants.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2012:GSR,
author = "Zhi-Guo Liu",
title = "{Gauss} summation and {Ramanujan}-type series for $ 1
/ \pi $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "289--297",
month = mar,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500169",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500169",
abstract = "Using some properties of the gamma function and the
well-known Gauss summation formula for the classical
hypergeometric series, we prove a four-parameter series
expansion formula, which can produce infinitely many
Ramanujan-type series for 1/\pi.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Echi:2012:KS,
author = "Othman Echi and Nejib Ghanmi",
title = "The {Korselt} set of $ p q $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "299--309",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500170",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500170",
abstract = "Let $ \alpha \in \mathbb {Z} \setminus \{ 0 \} $. A
positive integer $N$ is said to be an $ \alpha
$-Korselt number ($ K_\alpha $-number, for short) if $
N \neq \alpha $ and $ N - \alpha $ is a multiple of $ p
- \alpha $ for each prime divisor $p$ of $N$. By the
{\em Korselt set\/} of N, we mean the set of all $
\alpha \in \mathbb {Z} \setminus \{ 0 \} $ such that
$N$ is a $ K_\alpha $-number; this set will be denoted
by $ \mathcal {KS}(N)$. Given a squarefree composite
number, it is not easy to provide its Korselt set and
Korselt weight both theoretically and computationally.
The simplest kind of squarefree composite number is the
product of two distinct prime numbers. Even for this
kind of numbers, the Korselt set is far from being
characterized. Let $p$, $q$ be two distinct prime
numbers. This paper sheds some light on.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sengun:2012:THN,
author = "Mehmet Haluk {\c{S}}eng{\"u}n",
title = "On the Torsion Homology of Non-Arithmetic Hyperbolic
Tetrahedral Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "311--320",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500182",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500182",
abstract = "Numerical data concerning the growth of torsion in the
first homology of congruence subgroups of
non-arithmetic hyperbolic tetrahedral groups are
collected. The data provide support the speculations of
Bergeron and Venkatesh on the growth of torsion
homology and the regulators for lattices in SL$_2$
({\mathbb{C}}).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cullinan:2012:SSA,
author = "John Cullinan",
title = "Symplectic Stabilizers with Applications to {Abelian}
Varieties",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "321--334",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500194",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500194",
abstract = "Fix a prime number \ell > 2 and let V be a
four-dimensional F$_{\ell }$-vector space. We classify
subgroups G of Sp(V) with the property that every g \in
G stabilizes a one-dimensional subspace of V, yet G
itself is not of parabolic type. This classification is
motivated by its application to the mod \ell
representation of abelian surfaces, following a program
outlined by Sutherland.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Akhtari:2012:UBN,
author = "Shabnam Akhtari",
title = "Upper Bounds for the Number of Solutions to Quartic
{Thue} Equations",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "335--360",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500200",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500200",
abstract = "We will give upper bounds for the number of integral
solutions to quartic Thue equations. Our main tool here
is a logarithmic curve \varphi (x, y) that allows us to
use the theory of linear forms in logarithms. This
paper improves the results of the author's earlier work
with Okazaki [The quartic Thue equations, {\em J.
Number Theory\/} 130(1) (2010) 40--60] by giving
special treatments to forms with respect to their
signature.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bundschuh:2012:TAI,
author = "Peter Bundschuh",
title = "Transcendence and Algebraic Independence of Series
Related to {Stern}'s Sequence",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "361--376",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500212",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500212",
abstract = "In this same journal, Coons published recently a paper
[The transcendence of series related to Stern's
diatomic sequence, {\em Int. J. Number Theory\/} 6
(2010) 211--217] on the function theoretical
transcendence of the generating function of the Stern
sequence, and the transcendence over {$ \mathbb {Q} $}
of the function values at all non-zero algebraic points
of the unit disk. The main aim of our paper is to prove
the algebraic independence over {$ \mathbb {Q} $} of
the values of this function and all its derivatives at
the same points. The basic analytic ingredient of the
proof is the hypertranscendence of the function to be
shown before. Another main result concerns the
generating function of the Stern polynomials. Whereas
the function theoretical transcendence of this function
of two variables was already shown by Coons, we prove
that, for every pair of non-zero algebraic points in
the unit disk, the function value either vanishes or is
transcendental.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Madritsch:2012:AFP,
author = "Manfred G. Madritsch",
title = "$q$-additive functions on polynomial sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "377--393",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500224",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500224",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lee:2012:PPF,
author = "Pak-Hin Lee and Alexandr Zamorzaev",
title = "Parity of the Partition Function and Traces of
Singular Moduli",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "395--409",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500236",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500236",
abstract = "We prove that the parity of the partition function is
given by the ``trace'' of the Hauptmodul for at points
of complex multiplication. Using Hecke operators, we
generalize this to relate the Hecke traces of to the
partition function modulo 2. We then prove that the
generating function for these Hecke traces is equal to
the logarithmic derivative of the level 6 Hilbert class
polynomial. Finally, we give a procedure involving
Hilbert class polynomials for computing the parity of
the partition function, and make some speculations
about the distribution of these universal polynomials
modulo class polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Young:2012:TTF,
author = "Justin Young",
title = "The twisted tensor {$L$}-function of {$ \mathrm
{GSp}_4$}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "411--470",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500248",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500248",
abstract = "The author gives an integral representation for the
twisted tensor {$L$}-function of a cuspidal, globally
generic automorphic representation of GSp$_4$ over a
quadratic extension E of a number field F with trivial
central character. He proves the Euler product
factorization of the global integral; computes the
unramified $L$-factor via explicit branching from
GL$_4$ to Sp$_4$ and shows it is equal to the
normalized unramified local integral; and proves the
absolute convergence and nonvanishing of all local
integrals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mayer:2012:SCG,
author = "Daniel C. Mayer",
title = "The second $p$-class group of a number field",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "471--505",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250025X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250025X",
abstract = "For a prime p \geq 2 and a number field K with
$p$-class group of type (p, p) it is shown that the
class, coclass, and further invariants of the
metabelian Galois group of the second Hilbert $p$-class
field of K are determined by the $p$-class numbers of
the unramified cyclic extensions N$_i$ |K, 1 \leq i
\leq p + 1, of relative degree p. In the case of a
quadratic field and an odd prime p \geq 3, the
invariants of G are derived from the $p$-class numbers
of the non-Galois subfields L$_i$ |{$ \mathbb {Q}$} of
absolute degree p of the dihedral fields N$_i$. As an
application, the structure of the automorphism group of
the second Hilbert 3-class field is analyzed for all
quadratic fields K with discriminant -10$^6$ < D <
10$^7$ and 3-class group of type (3, 3) by computing
their principalization types. The distribution of these
metabelian 3-groups G on the coclass graphs, 1 \leq r
\leq 6, in the sense of Eick and Leedham-Green is
investigated.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wang:2012:HPF,
author = "Julie Tzu-Yueh Wang",
title = "{Hensley}'s Problem for Function Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "507--524",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500261",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500261",
abstract = "B{\"u}chi's square problem asks if there exists a
positive integer M such that all x$_1$, \ldots, x$_M$
\in {\mathbb{Z}} satisfying the equations for all 3
\leq r \leq M must also satisfy for some integer x and
for all 1 \leq r \leq M. Hensley's problem asks if
there exists a positive integer M such that, for any
integers \nu and a, if (\nu + r)$^2$- a is a square for
all 1 \leq r \leq M, then a = 0. It is not difficult to
see that a positive answer to Hensley's problem implies
a positive answer to B{\"u}chi's square problem. One
can ask a more general version of Hensley's problem by
replacing the square power by an nth power for any
integer n \geq 2 which is called Hensley's problem for
nth powers. In this paper, we will study Hensley's
problem for nth powers over function fields of any
characteristic.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2012:NVD,
author = "Sheng-Chi Liu",
title = "A Note on the Variance of the Distribution of
{Heegner} Points",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "525--529",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500273",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500273",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Preparata:2012:RPI,
author = "Franco P. Preparata and Roberto Vacca",
title = "On the Representation of the Powers of Integers in Any
Prime Base",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "531--541",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500285",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500285",
abstract = "This paper addresses the distribution of digits in the
positional representation of powers of integers, a
problem with a long history, and presents a complete
solution when the representation base is a prime
number. For any given base and exponent, the powers are
viewed as a semi-infinite array whose rows are indexed
by the nonnegative integers and whose columns are
indexed by the representation positions. By using
arguments of elementary number theory, the positions of
the array are classified in a manner permitting their
enumeration. Since each column is a periodic sequence,
the distribution is expressed in terms of the number of
occurrences (frequency) of each digit in a period.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{VanGorder:2012:GTP,
author = "Robert A. {Van Gorder}",
title = "{Glaisher}-Type Products Over the Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "543--550",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500297",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500297",
abstract = "In this short paper, we demonstrate the computation of
certain Glaisher-type products over the primes by
differentiation of the Euler product identity. We are
able to give a formula for the logarithmic derivative
of \zeta (x) in terms of this product, in addition to
some other interesting identities.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Martinet:2012:BMV,
author = "Jacques Martinet and Achill Sch{\"u}rmann",
title = "Bases of Minimal Vectors in Lattices, {III}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "2",
pages = "551--567",
month = mar,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500303",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:27 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500303",
abstract = "We prove that all Euclidean lattices of dimension n
\leq 9 which are generated by their minimal vectors,
also possess a basis of minimal vectors. By providing a
new counterexample, we show that this is not the case
for all dimensions n \geq 10.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Viguie:2012:GUM,
author = "St{\'e}phane Vigui{\'e}",
title = "Global Units Modulo Elliptic Units and Ideal Class
Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "569--588",
month = may,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500315",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500315",
abstract = "Let p be a prime number, and let k be an imaginary
quadratic number field in which p decomposes into two
distinct primes {$ \mathfrak {p} $} and. Let k$_{\infty
}$ be the unique {\mathbb{Z}}$_p$ extension of k which
is unramified outside of {$ \mathfrak {p} $}, and let $
K_{\infty }$ be a finite extension of k$_{\infty }$,
abelian over k. Following closely the ideas of Belliard
in [1], we prove that in $ K_{\infty }$, the projective
limit of the $p$-class group and the projective limit
of units modulo elliptic units share the same \mu
invariant and the same \lambda -invariant. We deduce
that a version of the classical main conjecture, which
is known to be true for p \notin {2, 3}, holds also for
p \in {2, 3} once we neglect the \mu invariants.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Li:2012:EFT,
author = "Xian-Jin Li",
title = "On the Explicit Formula in the Theory of Prime
Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "589--597",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500327",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500327",
abstract = "In [Complements to Li's criterion for the Riemann
hypothesis, {\em J. Number Theory\/} 77 (1999)
274--287] Bombieri and Lagarias observed the remarkable
identity [1 - (1 - 1/s)$^n$ ] + [1 - (1 - 1/(1 -
s))$^n$ ] = [1 - (1 - 1/s)$^n$ ]\cdot [1 - (1 - 1/(1 -
s))$^n$ ], and pointed out that the positivity in Li's
criterion [The positivity of a sequence of numbers and
the Riemann hypothesis, {\em J. Number Theory\/} 65
(1997) 325--333] has the same meaning as in Weil's
criterion [Sur les ``formules explicites'' de la
th{\'e}orie des nombres premiers, in {\em Oeuvres
Scientifiques, Collected Paper\/}, Vol. II
(Springer-Verlag, New York, 1979), pp. 48--61]. Let
\lambda$_n$ = $ \sum_{\rho }$ [1 - (1 - 1/\rho)$^n$ ]
for n = 1, 2, \ldots, where \rho runs over the complex
zeros of the Riemann zeta function \zeta (s). In this
note, a certain truncation of \lambda$_n$ is expressed
as Weil's explicit formula [Sur les ``formules
explicites'' de la th{\'e}orie des nombres premiers, in
{\em Oeuvres Scientifiques, Collected Paper\/}, Vol. II
(Springer-Verlag, New York, 1979), pp. 48--61] for each
positive integer n. By using the Bombieri and Lagarias'
identity, we prove that the positivity of these
truncations implies the Riemann hypothesis. If these
truncations have suitable upper bounds, we prove that
all nontrivial zeros of the Riemann zeta function lie
on the critical line.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Carney:2012:PEF,
author = "Alexander Carney and Anastassia Etropolski and Sarah
Pitman",
title = "Powers of the Eta-Function and {Hecke} Operators",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "599--611",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500339",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500339",
abstract = "Half-integer weight Hecke operators and their distinct
properties play a major role in the theory surrounding
partition numbers and Dedekind's eta-function.
Generalizing the work of Ono in [K. Ono, The partition
function and Hecke operators, {\em Adv. Math.\/} 228
(2011) 527--534], here we obtain closed formulas for
the Hecke images of all negative powers of the
eta-function. These formulas are generated through the
use of Faber polynomials. In addition, congruences for
a large class of powers of Ramanujan's Delta-function
are obtained in a corollary. We further exhibit a fast
calculation for many large values of vector partition
functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Felix:2012:GTD,
author = "Adam Tyler Felix",
title = "Generalizing the {Titchmarsh} Divisor Problem",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "613--629",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500340",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500340",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chen:2012:DPN,
author = "Zhixiong Chen and Arne Winterhof",
title = "On the Distribution of Pseudorandom Numbers and
Vectors Derived from {Euler--Fermat} Quotients",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "631--641",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500352",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500352",
abstract = "We study the distribution of $s$-dimensional vectors
of consecutive Euler--Fermat quotients modulo a
composite $m$. More precisely, we prove two different
discrepancy bounds for $ s = 1$ and $ s > 1$ based on
the celebrated Burgess bound and on bounds on the
number of zeros of a polynomial modulo $m$,
respectively. The results extend some known bounds for
Fermat quotients modulo a prime of Ostafe and
Shparlinski. However, the case of composite modulus
brings some interesting twists.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tsai:2012:SCIa,
author = "Mu-Tsun Tsai and Alexandru Zaharescu",
title = "On the Sum of Consecutive Integers in Sequences",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "643--652",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500364",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500364",
abstract = "Let A be a set of natural numbers, r$_A$ (n) be the
number of ways to represent n as a sum of consecutive
elements in A, and M$_A$ (x) := $ \sum_{n \leq x}$
r$_A$ (n). Under various circumstances, we show that
M$_{ \mathbb {N} }$ (x) \sim \sum M$_{A i}$ (x), where
\mathbb{N} = \sqcup A$_i$ is a partition of \mathbb{N}.
In particular, we prove that the asymptotic formula
holds when the A$_i$ s are chosen such that A$_i$ = {n
\in \mathbb{N} : f(n) = i}, where f(n) can be one of
the following: (1) f(n) = \Omega (n), (2) f(n) = d(n),
(3) f(n) = r$_{ \mathbb {N} }$ (n), (4) (assuming the
Riemann Hypothesis) f(n) = \Vert n\Vert := min{\mid n -
p\mid : p \in {\u{2}119}} (the distance to the set of
primes).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baruah:2012:ISC,
author = "Nayandeep Deka Baruah and Bipul Kumar Sarmah",
title = "Identities for Self-Conjugate $7$- and $9$-Core
Partitions",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "653--667",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500376",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500376",
abstract = "By employing identities for Ramanujan's theta
functions, we show that asc$_7$ (8n + 7) = 0 and
asc$_9$ (8n + 10) = asc$_9$ (2n), where asc$_t$ (n)
denotes the number of t-core partitions of n that are
self-conjugates.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ulas:2012:APS,
author = "Maciej Ulas",
title = "Arithmetic Properties of the Sequence of Degrees of
{Stern} Polynomials and Related Results",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "669--687",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500388",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500388",
abstract = "Let B$_n$ (t) be an nth Stern polynomial and let e(n)
= deg B$_n$ (t) be its degree. In this note we continue
our study started in [On certain arithmetic properties
of Stern polynomials, {\em Publ. Math. Debrecen\/}
79(1--2) (2011) 55--81] of the arithmetic properties of
the sequence of Stern polynomials and the sequence. We
also study the sequence d(n) = ord$_{t = 0}$ B$_n$ (t).
Among other things we prove that d(n) = \nu (n), where
\nu (n) is the maximal power of 2 which divides the
number n. We also count the number of the solutions of
the equations e(m) = i and e(m) - d(m) = i in the
interval [1, 2$^n$ ]. We also obtain an interesting
closed expression for a certain sum involving Stern
polynomials.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Halupczok:2012:NBL,
author = "Karin Halupczok",
title = "A New Bound for the Large Sieve Inequality with Power
Moduli",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "689--695",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250039X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250039X",
abstract = "We give a new bound for the large sieve inequality
with power moduli q$^k$ that is uniform in k. The proof
uses a new theorem due to Wooley from his work
[Vinogradov's mean value theorem via efficient
congruencing, to appear in {\em Ann. of Math.\/} ] on
efficient congruencing.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Friedman:2012:SVD,
author = "Eduardo Friedman and Aldo Pereira",
title = "Special Values of {Dirichlet} Series and Zeta
Integrals",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "697--714",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500406",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500406",
abstract = "For $f$ and $g$ polynomials in $p$ variables, we
relate the special value at a non-positive integer $ s
= N$, obtained by analytic continuation of the
Dirichlet series, to special values of zeta integrals $
Z(s; f, g) = \int_{x \in [0, \infty)^p} g(x) f(x)^{-s}
\, d x (\Re (s) \gg 0)$. We prove a simple relation
between $ \zeta ( - N; f, g)$ and $ Z( - N; f_a, g_a)$,
where for $ a \in \mathbb {C}^p$, $ f_a(x)$ is the
shifted polynomial $ f_a(x) = f(a + x)$. By direct
calculation we prove the product rule for zeta
integrals at $ s = 0$, $ \degree (f h) \cdot Z(0; f h,
g) = \degree (f) \cdot Z(0; f, g) + \degree (h) \cdot
Z(0; h, g)$, and deduce the corresponding rule for
Dirichlet series at $ s = 0$, $ \degree (f h) \cdot
\zeta (0; f h, g) = \degree (f) \cdot \zeta (0; f, g) +
\degree (h) \cdot \zeta (0; h, g)$. This last formula
generalizes work of Shintani and Chen--Eie.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Khuri-Makdisi:2012:MIE,
author = "Kamal Khuri-Makdisi",
title = "Moduli Interpretation of {Eisenstein} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "715--748",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500418",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500418",
abstract = "Let \ell \geq 3. Using the moduli interpretation, we
define certain elliptic modular forms of level \Gamma
(\ell) over any field k where 6\ell is invertible and k
contains the \ell th roots of unity. These forms
generate a graded algebra, which, over C, is generated
by the Eisenstein series of weight 1 on \Gamma (\ell).
The main result of this article is that, when k = C,
the ring contains all modular forms on \Gamma (\ell) in
weights \geq 2. The proof combines algebraic and
analytic techniques, including the action of Hecke
operators and nonvanishing of {$L$}-functions. Our
results give a systematic method to produce models for
the modular curve X(\ell) defined over the \ell th
cyclotomic field, using only exact arithmetic in the
\ell -torsion field of a single Q-rational elliptic
curve E$^0$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hulse:2012:SFC,
author = "Thomas A. Hulse and E. Mehmet Kiral and Chan Ieong
Kuan and Li-Mei Lim",
title = "The Sign of {Fourier} Coefficients of Half-Integral
Weight Cusp Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "749--762",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250042X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250042X",
abstract = "From a result of Waldspurger [W. Kohnen and D. Zagier,
Values of $L$-series of modular forms at the center of
the critical strip, {\em Invent. Math.\/} 64 (1981)
175--198], it is known that the normalized Fourier
coefficients a(m) of a half-integral weight holomorphic
cusp eigenform {$ \mathfrak {f} $} are, up to a finite
set of factors, one of when m is square-free and f is
the integral weight cusp form related to {$ \mathfrak
{f} $} by the Shimura correspondence [G. Shimura, On
modular forms of half-integral weight, {\em Ann. of
Math.\/} 97 (1973) 440--481]. In this paper we address
a question posed by Kohnen: which square root is a(m)?
In particular, if we look at the set of a(m) with m
square-free, do these Fourier coefficients change sign
infinitely often? By partially analytically continuing
a related Dirichlet series, we are able to show that
this is so.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Collas:2012:AGT,
author = "Benjamin Collas",
title = "Action of a {Grothendieck--Teichm{\"u}ller} group on
torsion elements of full {Teichm{\"u}ller} modular
groups of genus one",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "763--787",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500431",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500431",
abstract = "In this paper we define a new version of
Grothendieck--Teichm{\"u}ller group defined by three
generalized equations coming from finite-order
diffeomorphisms, and we prove that it is isomorphic to
the known version I\Gamma of the
Grothendieck--Teichm{\"u}ller defined in [H. Nakamura
and L. Schneps, On a subgroup of the
Grothendieck--Teichm{\"u}ller group acting on the tower
of profinite Teichm{\"u}ller modular groups, {\em
Invent. Math.\/} 141 (2000) 503--560]. We show that
acts on the full mapping class groups for 2g - 2 + n >
0. We then prove that the conjugacy classes of
prime-order torsion of are exactly the {\em discrete\/}
prime-order ones of. Using this we prove that acts on
prime-order torsion elements of in a particular way
called \lambda conjugacy, analogous to the Galois
action on inertia.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Luca:2012:LCD,
author = "Florian Luca and Paul Thomas Young",
title = "On the Log-Concavity of the Degenerate {Bernoulli}
Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "789--800",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500443",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500443",
abstract = "The degenerate Bernoulli numbers \beta$_n$ (\lambda)
are polynomials with rational coefficients of degree n
in the variable \lambda, which arise in several
combinatorial settings. An appropriate change of
variable transforms \beta$_n$ (\lambda) into a
polynomial whose coefficients are all positive. Here,
we prove that this transformed polynomial is
log-concave, and therefore unimodal. As a consequence,
we deduce bounds on the absolute values of the roots of
\beta$_n$ (\lambda).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Budarina:2012:PNW,
author = "Natalia Budarina and Hugh O'Donnell",
title = "On a Problem of {Nesterenko}: When Is the Closest Root
of a Polynomial a Real Number?",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "801--811",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500455",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500455",
abstract = "Let P be an integer polynomial of height H. In this
article we investigate the value of w where, if |P(x)|
< H$^{-w}$, then the root \alpha$_1$ of P closest to x
is real. We prove that for w > 2n - 3, and sufficiently
large H the root \alpha$_1$ belongs to the field of
real numbers and we also bound the distance between x
and \alpha$_1$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhang:2012:DE,
author = "Zhongfeng Zhang and Pingzhi Yuan",
title = "On the {Diophantine} equation $ a x^y + b y^z + c z^x
= 0 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "813--821",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500467",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500467",
abstract = "Let $ a, b, c $ be integers. In this paper, we prove
the integer solutions of the equation $ a x^y + b y^z +
c z^x = 0 $ satisfy $ \{ m a x|x|, |y|, |z| \} \leq 2
\max \{ a, b, c \} $ when $ a, b, c $ are odd positive
integers, and when $ a = b = 1 $, $ c = - 1 $, the
positive integer solutions of the equation satisfy $
\max \{ x, y, z \} < \exp (\exp (\exp (5))) $.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Marko:2012:NDD,
author = "Franti{\v{s}}ek Marko and {\v{S}}tefan Porubsk{\'y}",
title = "A Note on Density and the {Dirichlet} Condition",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "823--830",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500479",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500479",
abstract = "Motivated by topological approaches to Euclid and
Dirichlet's theorems on infinitude of primes, we
introduce and study coprime topologies on a commutative
ring R with an identity and without zero divisors. For
infinite semiprimitive commutative domain R of finite
character (i.e. every nonzero element of R is contained
in at most finitely many maximal ideals of R), we
characterize its subsets A for which the Dirichlet
condition, requiring the existence of infinitely many
pairwise nonassociated elements from A in every open
set in the invertible topology, is satisfied.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kinjo:2012:HSA,
author = "Kensaku Kinjo and Yuken Miyasaka",
title = "Hypergeometric series and arithmetic--geometric mean
over $2$-adic fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "831--844",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500480",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
MRclass = "11S80 (11G20 33C05)",
MRnumber = "2904934",
bibdate = "Tue Mar 14 07:52:56 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/agm.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500480",
abstract = "Dwork proved that the Gaussian hypergeometric function
on $p$-adic numbers can be extended to a function which
takes values of the unit roots of ordinary elliptic
curves over a finite field of characteristic $ p \geq
3$. We present an analogous theory in the case $ p =
2$. As an application, we give a relation between the
canonical lift and the unit root of an elliptic curve
over a finite field of characteristic $2$ by using the
$2$-adic arithmetic--geometric mean.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kluners:2012:DNF,
author = "J{\"u}rgen Kl{\"u}ners",
title = "The Distribution of Number Fields with Wreath Products
as {Galois} Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "3",
pages = "845--858",
month = may,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500492",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500492",
abstract = "Let G be a wreath product of the form C$_2$ \wr H,
where C$_2$ is the cyclic group of order 2. Under mild
conditions for H we determine the asymptotic behavior
of the counting functions for number fields K/k with
Galois group G and bounded discriminant. Those counting
functions grow linearly with the norm of the
discriminant and this result coincides with a
conjecture of Malle. Up to a constant factor these
groups have the same asymptotic behavior as the
conjectured one for symmetric groups.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Knopp:2012:RPG,
author = "Marvin Knopp and Geoffrey Mason",
title = "Revisions to {``Parabolic Generalized Modular Forms
and Their Characters''}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "859--864",
month = jun,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500509",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See \cite{Knopp:2009:PGM}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500509",
abstract = "The paper ``Parabolic Generalized Modular Forms and
Their Characters'' which previously appeared in this
journal, contained several anomalies in Sec. 3,
``Structure of '', arising from a mishandling of
complex powers of the functions denoted F(\tau ). Here,
we provide corrected proofs of the principle results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Jameson:2012:RRC,
author = "Marie Jameson",
title = "A Refinement of {Ramanujan}'s Congruences Modulo
Powers of $7$ and $ 11$",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "865--879",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500510",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500510",
abstract = "Ramanujan's famous congruences for the partition
function modulo powers of 5, 7, and 11 have inspired
much further research. For example, in 2002 Lovejoy and
Ono found subprogressions of 5$^j$ n + \beta$_5$ (j)
for which Ramanujan's congruence mod 5$^j$ could be
strengthened to a statement modulo 5$^{j + 1}$. Here we
provide the analogous results modulo powers of 7 and
11. We require the arithmetic properties of two special
elliptic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Matar:2012:SGG,
author = "Ahmed Matar",
title = "{Selmer} Groups and Generalized Class Field Towers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "881--909",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500522",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500522",
abstract = "This paper proves a control theorem for the
$p$-primary Selmer group of an abelian variety with
respect to extensions of the form: Maximal pro-p
extension of a number field unramified outside a finite
set of primes R which does not include any primes
dividing p in which another finite set of primes S
splits completely. When the Galois group of the
extension is not $p$-adic analytic, the control theorem
gives information about $p$-ranks of Selmer and
Tate--Shafarevich groups of the abelian variety. The
paper also discusses what can be said in regards to a
control theorem when the set R contains all the primes
of the number field dividing p.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Goins:2012:PHR,
author = "Edray Herber Goins and Kevin Mugo",
title = "Points on Hyperbolas at Rational Distance",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "911--922",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500534",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500534",
abstract = "Richard Guy asked for the largest set of points which
can be placed in the plane so that their pairwise
distances are rational numbers. In this article, we
consider such a set of rational points restricted to a
given hyperbola. To be precise, for rational numbers a,
b, c, and d such that the quantity D = (ad -
bc)/(2a$^2$) is defined and non-zero, we consider
rational distance sets on the conic section axy + bx +
cy + d = 0. We show that, if the elliptic curve Y$^2$ =
X$^3$- D$^2$ X has infinitely many rational points,
then there are infinitely many sets consisting of four
rational points on the hyperbola such that their
pairwise distances are rational numbers. We also show
that any rational distance set of three such points can
always be extended to a rational distance set of four
such points.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Maurischat:2012:COS,
author = "Kathrin Maurischat",
title = "{Casimir} Operators for Symplectic Groups",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "923--932",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500546",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500546",
abstract = "We give a full set of generators for the center of the
universal enveloping Lie algebra of the symplectic
group of arbitrary genus. They are of trace type and
are given in terms of a basis chosen such that the
action on representations of given K-type becomes
transparent. We give examples for the latter.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Awtrey:2012:DAF,
author = "Chad Awtrey",
title = "Dodecic $3$-Adic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "933--944",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500558",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500558",
abstract = "Let n be an integer and p be a prime number. An
important problem in number theory is to classify the
degree n extensions of the $p$-adic numbers through
their arithmetic invariants. The most difficult cases
arise when p divides n and n is composite. In this
paper, we consider the case n = 12 and p = 3; the
degrees n < 12 having previously been determined.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Barman:2012:CVG,
author = "Rupam Barman and Gautam Kalita",
title = "Certain Values of {Gaussian} Hypergeometric Series and
a Family of Algebraic Curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "945--961",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250056X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250056X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{ElBasraoui:2012:REF,
author = "Abdelkrim {El Basraoui} and Abdellah Sebbar",
title = "Rational Equivariant Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "963--981",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500571",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500571",
abstract = "We investigate the notion of equivariant forms as
functions on the upper half-plane commuting with the
action of a discrete group. We put an emphasis on the
rational equivariant forms for a modular subgroup that
are parametrized by generalized modular forms.
Furthermore, we study this parametrization when the
modular subgroup is of genus zero as well as their
behavior under the effect of the Schwarz derivative.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hentschel:2012:CEU,
author = "Michael Hentschel and Aloys Krieg and Gabriele Nebe",
title = "On the Classification of Even Unimodular Lattices with
a Complex Structure",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "983--992",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500583",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500583",
abstract = "This paper classifies the even unimodular lattices
that have a structure as a Hermitian -lattice of rank r
\leq 12 for rings of integers in imaginary quadratic
number fields K of class number 1. The Hermitian theta
series of such a lattice is a Hermitian modular form of
weight r for the full modular group, therefore we call
them theta lattices. For arbitrary imaginary quadratic
fields we derive a mass formula for the principal genus
of theta lattices which is applied to show completeness
of the classifications.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Williams:2012:FSC,
author = "Kenneth S. Williams",
title = "{Fourier} Series of a Class of Eta Quotients",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "993--1004",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500595",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500595",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{VanOrder:2012:QAF,
author = "Jeanine {Van Order}",
title = "On the quaternionic $p$-adic {$L$}-functions
associated to {Hilbert} modular eigenforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1005--1039",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500601",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See erratum \cite{VanOrder:2016:EQA}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500601",
abstract = "We construct $p$-adic {$L$}-functions associated to
cuspidal Hilbert modular eigenforms of parallel weight
two in certain dihedral or anticyclotomic extensions
via the Jacquet--Langlands correspondence, generalizing
works of Bertolini--Darmon, Vatsal and others. The
construction given here is adelic, which allows us to
deduce a precise interpolation formula from a
Waldspurger-type theorem, as well as a formula for the
dihedral \mu -invariant. We also make a note of
Howard's non-vanishing criterion for these $p$-adic
{$L$}-functions, which can be used to reduce the
associated Iwasawa main conjecture to a certain
non-triviality criterion for families of $p$-adic
{$L$}-functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Yao:2012:NRI,
author = "Olivia X. M. Yao and Ernest X. W. Xia",
title = "The Number of Representations of an Integer As a Sum
Involving Generalized Pentagonal Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1041--1056",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500613",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500613",
abstract = "In this paper, using the (p, k)-parametrization of
theta functions given by Alaca, Alaca and Williams, we
establish some theta function identities. From these
identities, we obtain some formulas for the number of
representations of a natural number as a sum of
quadratic polynomials involving generalized pentagonal
numbers. In particular, we derive a formula for the
number of representations of a natural number as a sum
of twelve generalized pentagonal numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hong:2012:AVS,
author = "Shaofang Hong and Jianrong Zhao and Wei Zhao",
title = "The $2$-Adic Valuations of {Stirling} Numbers of the
Second Kind",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1057--1066",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500625",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500625",
abstract = "In this paper, we investigate the 2-adic valuations of
the Stirling numbers S(n, k) of the second kind. We
show that v$_2$ (S(4i, 5)) = v$_2$ (S(4i + 3, 5)) if
and only if i \nequiv 7 (mod 32). This confirms a
conjecture of Amdeberhan, Manna and Moll raised in
2008. We show also that v$_2$ (S(2$^n$ + 1, k + 1)) =
s$_2$ (n) - 1 for any positive integer n, where s$_2$
(n) is the sum of binary digits of n. It proves another
conjecture of Amdeberhan, Manna and Moll.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Muetzel:2012:NLB,
author = "Bjoern Muetzel",
title = "A New Lower Bound for {Hermite}'s Constant for
Symplectic Lattices",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1067--1080",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500637",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500637",
abstract = "In this paper we give an improved lower bound on
Hermite's constant $ \delta_{2g} $ for symplectic
lattices in even dimensions $ (g = 2 n) $ by applying a
mean-value argument from the geometry of numbers to a
subset of symmetric lattices. We obtain only a slight
improvement. However, we believe that the method
applied has further potential. Furthermore, in this
paper we present new families of highly symmetric
(symplectic) lattices, which occur in dimensions of
powers of two. The lattices in dimension $ 2^n $ are
constructed with the help of a multiplicative matrix
group isomorphic to $ (\mathbb {Z}_{2^n}, +) $. We
furthermore show the connection of these lattices with
the circulant matrices and the Barnes--Wall lattices.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mestrovic:2012:PCH,
author = "Romeo Me{\v{s}}trovi{\'c}",
title = "Proof of a Congruence for Harmonic Numbers Conjectured
by {Z.-W. Sun}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1081--1085",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500649",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500649",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fanali:2012:NRP,
author = "Stefania Fanali and Massimo Giulietti",
title = "On the Number of Rational Points of Generalized
{Fermat} Curves Over Finite Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1087--1097",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500650",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500650",
abstract = "The St{\"o}hr--Voloch approach has been largely used
to deal with the classical problem of estimating the
number of rational points of a Fermat curve over a
finite field. The same method actually applies to any
curve admitting as an automorphism group the direct
product of two cyclic groups C$_1$ and C$_2$ of the
same size k, and such that the quotient curves with
respect to both C$_1$ and C$_2$ are rational. In this
paper such a curve is called a generalized Fermat
curve. Our main achievement is that of extending some
known results on Fermat curves to generalized Fermat
curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tanabe:2012:NVD,
author = "Naomi Tanabe",
title = "Non-Vanishing of Derivatives of {$L$}-Functions
Attached to {Hilbert} Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "4",
pages = "1099--1105",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500662",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500662",
abstract = "This paper is to show a non-vanishing property of the
derivative of certain {$L$}-functions. For certain
primitive holomorphic Hilbert modular forms, if the
central critical value of the standard {$L$}-function
does not vanish, then neither does its derivative. This
is a generalization of a result by Gun, Murty and Rath
in the case of elliptic modular forms. Some
applications in transcendental number theory deduced
from this result are discussed as well.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kim:2012:FGK,
author = "Henry H. Kim and Kyu-Hwan Lee",
title = "A Family of Generalized {Kac--Moody} Algebras and
Deformation of Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1107--1131",
month = aug,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500674",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500674",
abstract = "We develop an analogue of Gindikin--Karpelevich
formula for a family of generalized Kac--Moody
algebras, attached to Borcherds--Cartan matrices
consisting of only one positive entry in the diagonal.
As an application, we obtain a deformation of Fourier
coefficients of modular forms such as the modular
j-function and Ramanujan \tau -function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kuhnlein:2012:WRS,
author = "Stefan K{\"u}hnlein",
title = "Well-Rounded Sublattices",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1133--1144",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500686",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500686",
abstract = "Given a lattice in the plane, we consider
zeta-functions encoding the number of well-rounded
sublattices of a given index. We are particularly
interested in the abscissa of convergence of this
function and show that the quality of convergence is
related to arithmeticity questions concerning the
ambient lattice. In particular, we discover that there
are infinitely many similarity classes of well-rounded
sublattices in a plane lattice if there is at least
one. This generalizes results about the rings of
Gaussian and of Eisenstein integers by Fukshansky and
his coauthors.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Haukkanen:2012:ANL,
author = "Pentti Haukkanen and Jorma K. Merikoski",
title = "Asymptotics for Numbers of Line Segments and Lines in
a Square Grid",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1145--1152",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500698",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500698",
abstract = "We present an asymptotic formula for the number of
line segments connecting q + 1 points of an n $ \times
$ n square grid, and a sharper formula, assuming the
Riemann hypothesis. We also present asymptotic formulas
for the number of lines through at least q points and,
respectively, through exactly q points of the grid. The
well-known case q = 2 is so generalized.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Flicker:2012:CTC,
author = "Yuval Z. Flicker and Dmitrii Zinoviev",
title = "Computation of a Twisted Character of a Small
Representation of {$ \mathrm {Gl}(3, E) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1153--1230",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500704",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500704",
abstract = "Let E/F be a quadratic extension of $p$-adic fields, p
\neq 2. Let be the involution of E over F. The
representation \pi of GL(3, E) normalizedly induced
from the trivial representation of the maximal
parabolic subgroup is invariant under the involution.
We compute --- by purely local means --- the \sigma
-twisted character of \pi. We show that it is \sigma
-unstable, namely its value at one \sigma
-regular-elliptic conjugacy class within a stable such
class is equal to negative its value at the other such
conjugacy class within the stable class, or zero when
the \sigma -regular-elliptic stable conjugacy class
consists of a single such conjugacy class. Further, we
relate this twisted character to the twisted endoscopic
lifting from the trivial representation of the
``unstable'' twisted endoscopic group U(2, E/F) of
GL(3, E). In particular \pi is \sigma -elliptic, that
is, is not identically zero on the \sigma -elliptic
set.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Najman:2012:EEC,
author = "Filip Najman",
title = "Exceptional Elliptic Curves Over Quartic Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1231--1246",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500716",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500716",
abstract = "We study the number of elliptic curves, up to
isomorphism, over a fixed quartic field K having a
prescribed torsion group T as a subgroup. Let T =
{\mathbb{Z}}/m{\mathbb{Z}}\oplus
{\mathbb{Z}}/n{\mathbb{Z}}, where m|n, be a torsion
group such that the modular curve X$_1$ (m, n) is an
elliptic curve. Let K be a number field such that there
is a positive and finite number of elliptic curves E
over K having T as a subgroup. We call such pairs (T,
K) {\em exceptional}. It is known that there are only
finitely many exceptional pairs when K varies through
all quadratic or cubic fields. We prove that when K
varies through all quartic fields, there exist
infinitely many exceptional pairs when T =
{\mathbb{Z}}/14{\mathbb{Z}} or
{\mathbb{Z}}/15{\mathbb{Z}} and finitely many
otherwise.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2012:WGP,
author = "Zhixin Liu",
title = "On {Waring--Goldbach} Problem for Fifth Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1247--1256",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500728",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500728",
abstract = "In this short paper, we investigate exceptional sets
in the Waring--Goldbach problem for fifth powers. For
example, we show that all but O(N$^{213 / 214}$)
integers subject to the necessary local conditions can
be represented as the sum of 11 fifth powers of primes.
This improves the previous result.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gomez-Molleda:2012:CNF,
author = "M. A. G{\'o}mez-Molleda and Joan-C. Lario",
title = "Class Number Formulas for Certain Bicyclic Biquadratic
Number Fields As Finite Sums Involving {Jacobi}
Elliptic Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1257--1270",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250073X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250073X",
abstract = "We give formulas for the class numbers of bicyclic
biquadratic number fields containing an imaginary
quadratic field of class number one. The class number
is expressed as a finite sum in terms of the basic
Jacobi elliptic functions, playing a similar role as
the trigonometric sine in Dirichlet classical class
number formula.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wang:2012:CNF,
author = "Q. H. Wang and J. J. Zhuang",
title = "On the critical number of finite groups of order $ p q
$",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1271--1279",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500741",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500741",
abstract = "Let G be a finite group and S be a subset of {G0}. We
call S an {\em additive basis of G\/} if every element
of G can be expressed as a sum over a non-empty subset
in some order. Let cr(G) be the smallest integer t such
that every subset of {G0} of cardinality t forms an
additive basis of G. In this paper, we determine cr(G)
for all groups G of order pq, where p, q are primes.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tsai:2012:SCIb,
author = "Mu-Tsun Tsai and Alexandru Zaharescu",
title = "On the Sum of Consecutive Integers in Sequences {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1281--1299",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500753",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500753",
abstract = "Let A be a sequence of natural numbers, r$_A$ (n) be
the number of ways to represent n as a sum of
consecutive elements in A, and M$_A$ (x) \coloneq $
\sum_{n \leq x}$ r$_A$ (n). We give a new short proof
of LeVeque's formula regarding M$_A$ (x) when A is an
arithmetic progression, and then extend the proof to
give asymptotic formulas for the case when A behaves
almost like an arithmetic progression, and also when A
is the set of primes in an arithmetic progression.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chatterjee:2012:SCM,
author = "Tapas Chatterjee",
title = "The Strong {Chowla--Milnor} Spaces and a Conjecture of
{Gun}, {Murty} and {Rath}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1301--1314",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500765",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500765",
abstract = "In a recent work, Gun, Murty and Rath formulated the
Strong Chowla--Milnor conjecture and defined the Strong
Chowla--Milnor space. In this paper, we proved a
non-trivial lower bound for the dimension of these
spaces. We also obtained a conditional improvement of
this lower bound and noted that an unconditional
improvement of this lower bound will lead to
irrationality of both \zeta (k) and \zeta (k)/\pi$^k$
for all odd positive integers k. Following Gun, Murty
and Rath, we define generalized Zagier spaces V$_p$ (K)
for multiple zeta values over a number field K. We
prove that the dimension of V$_{4d + 2}$ (K) for d \geq
1, is at least 2, assuming a conjecture of Gun, Murty
and Rath.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lezowski:2012:ENE,
author = "Pierre Lezowski",
title = "Examples of Norm-{Euclidean} Ideal Classes",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "5",
pages = "1315--1333",
month = aug,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500777",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:28 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500777",
abstract = "In this paper, we study the notion of norm-Euclidean
ideal class, which was defined by Lenstra [Euclidean
ideal classes, {\em Ast{\'e}risque\/} {\u{0}0a0}4061
(1979) 121--131]. Using a slight modification of an
algorithm determining among other properties the
Euclidean minimum described in [P. Lezowski,
Computation of the Euclidean minimum of algebraic
number fields, preprint (2011);
http://hal.archives-ouvertes.fr/hal-00632997/en/], we
give new examples of number fields with norm-Euclidean
ideal classes. Extending the results of Cioffari [The
Euclidean condition in pure cubic and complex quartic
fields, {\em Math. Comput.\/} {\u{0}0a0}4033 (1979)
389--398], we also establish the complete list of pure
cubic number fields which admit a norm-Euclidean ideal
class. Finally, we show that , which is known to admit
a non-principal Euclidean ideal class, has no
norm-Euclidean ideal class.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Shlapentokh:2012:ECP,
author = "Alexandra Shlapentokh",
title = "Elliptic curve points and {Diophantine} models of {$
\mathbb {Z} $} in large subrings of number fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1335--1365",
month = sep,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500789",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500789",
abstract = "Let K be a number field such that there exists an
elliptic curve E of rank one over K. For a set of
primes of K, let . Let P \in E(K) be a generator of
E(K) modulo the torsion subgroup. Let (x$_n$ (P), y$_n$
(P)) be the affine coordinates of [n]P with respect to
a fixed Weierstrass equation of E. We show that there
exists a set of primes of K of natural density one such
that in multiplication of indices (with respect to some
fixed multiple of P) is existentially definable and
therefore these indices can be used to construct a
Diophantine model of {\mathbb{Z}}. We also show that
{\mathbb{Z}} is definable over using just one universal
quantifier. Both the construction of a Diophantine
model using the indices and the first-order definition
of {\mathbb{Z}} can be lifted to the integral closure
of in any infinite extension $ K_{\infty }$ of K as
long as E(K$_{\infty }$) is finitely generated and of
rank one.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wakabayashi:2012:NSQ,
author = "Isao Wakabayashi",
title = "Number of Solutions for Quartic Simple {Thue}
Equations",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1367--1386",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500790",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500790",
abstract = "Let F(X, Y) = bX$^4$- aX$^3$ Y - 6bX$^2$ Y$^2$ + a
{\em XY\/}$^3$ + bY$^4$ \in Z[X, Y]. We show that the
number of solutions for the Thue equation F(x, y) = \pm
1 is 0 or 4 except for a few already known cases. To
obtain an upper bound for the size of solutions, we use
Pad{\'e} approximation method. To obtain a lower bound
for the size of solutions, we construct a continued
fraction with positive or negative rational partial
quotients. This construction is carried out carefully
by using special properties of the form F. Combining
these lower and upper bounds, we obtain the result.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Basic:2012:DPD,
author = "Bojan Ba{\v{s}}i{\'c}",
title = "On $d$-digit palindromes in different bases: the
number of bases is unbounded",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1387--1390",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500819",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500819",
abstract = "The following problem was posed in [E. H. Goins,
Palindromes in different bases: a conjecture of J.
Ernest Wilkins, {\em Integers\/} {\u{0}0a0}409 (2009)
725--734]: ``What is the largest list of bases b for
which an integer N \geq 10 is a d-digit palindrome base
b for every base in the list?'' We show that it is
possible to construct such a list as large as we
please. Furthermore, we show that it is possible to
construct such arbitrarily large list for {\em any\/}
given d.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gunaydin:2012:RSP,
author = "Ayhan G{\"u}naydin",
title = "Rational Solutions of Polynomial--Exponential
Equations",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1391--1399",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500820",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500820",
abstract = "We give a description of solutions of
polynomial-exponential equations where the variables
vary over rational numbers. Using this, we also prove a
finiteness result.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Greve:2012:RPS,
author = "Christian Greve and Sebastian Pauli",
title = "Ramification Polygons, Splitting Fields, and {Galois}
Groups of {Eisenstein} Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1401--1424",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500832",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500832",
abstract = "Let \varphi (x) be an Eisenstein polynomial of degree
n over a local field and let \alpha be a root of
\varphi (x). The Newton polygon of \rho (x) = \varphi
(\alpha x+\alpha)/\alpha$^n$ is called the ramification
polygon of \varphi (x). We attach an additional
invariant, the segmental inertia degree, to each
segment of the ramification polygon and use the slopes
of the segments and their segmental inertia degrees to
describe the splitting field of \varphi (x).
Furthermore we present a method for determining the
Galois group of \varphi (x) when the ramification
polygon consists of one segment.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Longo:2012:NCT,
author = "Matteo Longo and Stefano Vigni",
title = "A Note on Control Theorems for Quaternionic {Hida}
Families of Modular Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1425--1462",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500856",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500856",
abstract = "We extend a result of Greenberg and Stevens on the
interpolation of modular symbols in Hida families to
the context of non-split rational quaternion algebras.
Both the definite case and the indefinite case are
considered.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lee:2012:DCN,
author = "Seok Hyeong Lee and Gyujin Oh",
title = "On the Distribution of Cyclic Number Fields of Prime
Degree",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1463--1475",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500868",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500868",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Busch:2012:LHE,
author = "Vincenz Busch and Jan Steffen M{\"u}ller",
title = "Local Heights on Elliptic Curves and Intersection
Multiplicities",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1477--1484",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250087X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250087X",
abstract = "In this short note we prove a formula for local
heights on elliptic curves over number fields in terms
of intersection theory on a regular model over the ring
of integers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Maharaj:2012:SMF,
author = "Hiren Maharaj",
title = "Spaces of Modular Forms and Algebraic Geometric
Codes",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1485--1502",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500881",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500881",
abstract = "For \ell = 2, 3, 5, we show that spaces of modular
forms M$_{2k}$ (\Gamma$_0$ (\ell$^n$)) are closely
related to a class of one-point codes from the
reduction of the modular tower {X$_0$ (\ell$^n$)}$_{n
\geq 2}$ (mod p) for primes p > \ell. Code construction
from the space of cusp form is also considered.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{ElBachraoui:2012:ASL,
author = "Mohamed {El Bachraoui}",
title = "Arithmetic Sums of {Liouville} Type Over Relatively
Prime Pairs",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1503--1512",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500893",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500893",
abstract = "We prove Liouville's type identities on sums of even
integer functions ranging over sets involving
relatively prime pairs.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Harrington:2012:FT,
author = "Joshua Harrington",
title = "On the factorization of the trinomials $ x^n + c x^{n
- 1} + d $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1513--1518",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250090X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250090X",
abstract = "In this paper we investigate the factorization of
trinomials of the form x$^n$ + cx$^{n - 1}$ + d \in
{\mathbb{Z}}[x]. We then use these results about
trinomials to prove results about the factorization of
polynomials of the form x$^n$ + c(x$^{n - 1}$ +\cdots +
x + 1) \in {\mathbb{Z}}[x].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Girstmair:2012:PCF,
author = "Kurt Girstmair",
title = "Periodic Continued Fractions and {Jacobi} Symbols",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1519--1525",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500911",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500911",
abstract = "Previously we proved the periodicity of the Jacobi
symbol for the convergents p$_k$ /q$_k$ of infinite
{\em purely\/} periodic continued fractions. The aim of
this note is to establish an analogous result for {\em
mixed\/} periodic continued fractions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Minculete:2012:CIA,
author = "Nicu{\c{s}}or Minculete",
title = "On Certain Inequalities About Arithmetic Functions
Which Use the Exponential Divisors",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1527--1535",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500923",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500923",
abstract = "The purpose of this paper is to present several
inequalities for the arithmetic functions
\sigma$^{(e)}$ and \tau$^{(e)}$. Among these, we have
the following:, for all n \geq 6,, for all n \geq 1. We
also prove that if the number is an e-perfect number,
then it has at least one exponent a$_i$ equal with 2.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Acquaah:2012:PFO,
author = "Peter Acquaah and Sergei Konyagin",
title = "On Prime Factors of Odd Perfect Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1537--1540",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500935",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500935",
abstract = "We prove that a prime factor q of an odd perfect
number x satisfies the inequality q < (3x)$^{1 / 3}$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhabitskaya:2012:CFO,
author = "E. N. Zhabitskaya",
title = "Continued Fractions with Odd Partial Quotients",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1541--1556",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500947",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500947",
abstract = "Every Euclidean algorithm is associated with a kind of
continued fraction representation of a number. The
representation associated with ``odd'' Euclidean
algorithm we will call ``odd'' continued fraction. We
consider the limit distribution function F(x) for
sequences of rationals with bounded sum of partial
quotients for ``odd'' continued fractions. In this
paper we prove certain properties of the function F(x).
Particularly this function is singular and satisfies a
number of functional equations. We also show that the
value F(x) can be expressed in terms of partial
quotients of the ``odd'' continued fraction
representation of a number x.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Adam:2012:AAF,
author = "David Adam",
title = "{Abel} Arithmetic Functions in Finite Characteristic",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "6",
pages = "1557--1568",
month = sep,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500959",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500959",
abstract = "We define Abel arithmetic functions in function fields
with positive characteristic. We prove that any Abel
arithmetic function with exponential type lesser than
is a polynomial, the bound being optimal. This provides
an analog of a Bertrandias' result. Some q-analogs are
considered too.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mantilla-Soler:2012:NFE,
author = "Guillermo Mantilla-Soler",
title = "On Number Fields with Equivalent Integral Trace
Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1569--1580",
month = nov,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112500807",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500807",
abstract = "Let K be a number field. The {\em integral trace
form\/} is the integral quadratic form given by $
\tr_{k / \mathbb {Q}} (x^2)|O_K $. In this article we
study the existence of non-conjugated number fields
with equivalent integral trace forms. As a corollary of
one of the main results of this paper, we show that any
two non-totally real number fields with the same
signature and same prime discriminant have equivalent
integral trace forms. Additionally, based on previous
results obtained by the author and the evidence
presented here, we conjecture that any two totally real
quartic fields of fundamental discriminant have
equivalent trace zero forms if and only if they are
conjugated.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{McCarthy:2012:EGH,
author = "Dermot McCarthy",
title = "Extending {Gaussian} hypergeometric series to the
$p$-adic setting",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1581--1612",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500844",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500844",
abstract = "We define a function which extends Gaussian
hypergeometric series to the $p$-adic setting. This new
function allows results involving Gaussian
hypergeometric series to be extended to a wider class
of primes. We demonstrate this by providing various
congruences between the function and truncated
classical hypergeometric series. These congruences
provide a framework for proving the supercongruence
conjectures of Rodriguez-Villegas.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hill:2012:AIM,
author = "Richard Hill and David Loeffler",
title = "$p$-adic interpolation of metaplectic forms of
cohomological type",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1613--1660",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500960",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500960",
abstract = "Let G be a reductive group over a number field k. It
is shown how Emerton's methods may be applied to the
problem of $p$-adically interpolating the metaplectic
forms on G, i.e. the automorphic forms on metaplectic
covers of G, as long as the metaplectic covers involved
split at the infinite places of k.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alaca:2012:QF,
author = "Ay{\c{s}}e Alaca and Kenneth S. Williams",
title = "On the quaternary forms $ x^2 + y^2 + 2 z^2 + 3 t^2 $,
$ x^2 + 2 y^2 + 2 z^2 + 6 t^2 $, $ x^2 + 3 y^2 + 3 z^2
+ 6 t^2 $ and $ 2 x^2 + 3 y^2 + 6 z^2 + 6 t^2 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1661--1686",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500972",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500972",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Felix:2012:PFR,
author = "Adam Tyler Felix and M. Ram Murty",
title = "A Problem of {Fomenko}'s Related to {Artin}'s
Conjecture",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1687--1723",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500984",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500984",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Andrade:2012:NMV,
author = "Julio Andrade",
title = "A Note on the Mean Value of {$L$}-Functions in
Function Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1725--1740",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112500996",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112500996",
abstract = "An asymptotic formula for the sum \sum L(1, \chi) is
established for a family of hyperelliptic curves of
genus g over a fixed finite field {$ \mathbb {F} $}$_q$
as g \rightarrow \infty making use of the analog of the
approximate functional equation for such
{$L$}-functions. As a corollary, we obtain a formula
for the average of the class number of the associated
rings.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kaczorowski:2012:STE,
author = "Jerzy Kaczorowski and Kazimierz Wiertelak",
title = "On the Sum of the Twisted {Euler} Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1741--1761",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250100X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250100X",
abstract = "We study an asymptotic formula for the sum of values
of the Euler \phi -function twisted by a real Dirichlet
character. The error term is split into the arithmetic
and the analytic part. The former is studied with
minimal use of analytic tools in contrast to the
latter, where the analysis depends heavily on the
distribution of the non-trivial zeros of the
corresponding Dirichlet {$L$}-function. The results of
the present paper are an extension of a recent work by
the authors, where the case of the classical Euler \phi
-Function has been studied. The present, more general
situation invites new technical difficulties. Not all
of them can be successfully overcome. For instance,
satisfactory omega results for the analytic part are
proved in the case of an even Dirichlet character only.
Nevertheless, a method providing good omega estimates
for the arithmetic part as well as for the complete
error term is developed. Moreover, it is noted that the
Riemann Hypothesis for the involved Dirichlet
{$L$}-function is equivalent to a sufficiently sharp
estimation of the analytic part. This shows in
particular that the arithmetic part can be much larger
than the corresponding analytic part.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Birmajer:2012:FPR,
author = "Daniel Birmajer and Juan B. Gil and Michael Weiner",
title = "Factoring polynomials in the ring of formal power
series over {$ \mathbb {Z} $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1763--1776",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501011",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501011",
abstract = "We consider polynomials with integer coefficients and
discuss their factorization properties in
{\mathbb{Z}}[[x]], the ring of formal power series over
{\mathbb{Z}}. We treat polynomials of arbitrary degree
and give sufficient conditions for their reducibility
as power series. Moreover, if a polynomial is reducible
over {\mathbb{Z}}[[x]], we provide an explicit
factorization algorithm. For polynomials whose constant
term is a prime power, our study leads to the
discussion of $p$-adic integers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Le:2012:CRS,
author = "T. A. Le and J. W. Sander",
title = "Convolutions of {Ramanujan} Sums and Integral
Circulant Graphs",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1777--1788",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501023",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501023",
abstract = "There exist several generalizations of the classical
Dirichlet convolution, for instance the so-called
A-convolutions analyzed by Narkiewicz. We shall connect
the concept of A-convolutions satisfying a weak form of
regularity and Ramanujan sums with the spectrum of
integral circulant graphs. These generalized Cayley
graphs, having circulant adjacency matrix and integral
eigenvalues, comprise a great amount of arithmetical
features. By use of our concept we obtain a
multiplicative decomposition of the so-called {\em
energy\/} of integral circulant graphs with
multiplicative divisor sets. This will be fundamental
for the study of open problems, in particular
concerning the detection of integral circulant graphs
with maximal or minimal energy.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pilehrood:2012:CCJ,
author = "Kh. Hessami Pilehrood and T. Hessami Pilehrood and R.
Tauraso",
title = "Congruences Concerning {Jacobi} Polynomials and
{Ap{\'e}ry}-Like Formulae",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "7",
pages = "1789--1811",
month = nov,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501035",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:29 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501035",
abstract = "Let p > 5 be a prime. We prove congruences modulo
p$^{3 - d}$ for sums of the general form and with d =
0, 1. We also consider the special case t = (-1)$^d$
/16 of the former sum, where the congruences hold
modulo p$^{5 - d}$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Lei:2012:NCA,
author = "Antonio Lei",
title = "Non-commutative $p$-adic {$L$}-functions for
supersingular primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1813--1830",
month = dec,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112501047",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501047",
abstract = "Let E/{$ \mathbb {Q} $} be an elliptic curve with good
supersingular reduction at p with a$_p$ (E) = 0. We
give a conjecture on the existence of analytic plus and
minus $p$-adic {$L$}-functions of E over the
{\mathbb{Z}}$_p$-cyclotomic extension of a finite
Galois extension of {$ \mathbb {Q}$} where p is
unramified. Under some technical conditions, we adopt
the method of Bouganis and Venjakob for $p$-ordinary CM
elliptic curves to construct such functions for a
particular non-abelian extension.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Muic:2012:ACN,
author = "Goran Mui{\'c}",
title = "On the Analytic Continuation and Non-Vanishing of
{$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1831--1854",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501059",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501059",
abstract = "Let \Gamma be a Fuchsian group of the first kind which
has a (regular) cusp at \infty such as \Gamma$_0$ (N).
In this paper we use Kohnen's kernel function for
\Gamma to analytically continue L(s, f) to the region
Re(s) > m/2, where f is a cuspidal modular form of
weight m \geq 5 attached to \Gamma. We study
non-vanishing of L(s, f) using our integral
non-vanishing criterion.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bui:2012:NVD,
author = "H. M. Bui",
title = "Non-Vanishing of {Dirichlet} {$L$}-Functions at the
Central Point",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1855--1881",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501060",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501060",
abstract = "Let \chi be a primitive Dirichlet character modulo q
and L(s, \chi) be the Dirichlet {$L$}-function
associated to \chi. Using a new two-piece mollifier we
show that L(\frac{1}{2}, \chi) \neq 0 for at least 34\%
of the characters in the family.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Moree:2012:NBT,
author = "Pieter Moree and Eugenia Ro{\c{s}}u",
title = "Non--{Beiter} ternary cyclotomic polynomials with an
optimally large set of coefficients",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1883--1902",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501072",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501072",
abstract = "Let l \geq 1 be an arbitrary odd integer and p, q and
r be primes. We show that there exist infinitely many
ternary cyclotomic polynomials \Phi$_{pqr}$ (x) with
l$^2$ + 3l + 5 \leq p < q < r such that the set of
coefficients of each of them consists of the p integers
in the interval [-(p - l - 2)/2, (p + l + 2)/2]. It is
known that no larger coefficient range is possible. The
Beiter conjecture states that the cyclotomic
coefficients a$_{pqr}$ (k) of \Phi$_{pqr}$ satisfy
|a$_{pqr}$ (k)| \leq (p + 1)/2 and thus the above
family contradicts the Beiter conjecture. The two
already known families of ternary cyclotomic
polynomials with an optimally large set of coefficients
(found by G. Bachman) satisfy the Beiter conjecture.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{MachHide:2012:WST,
author = "Tomoya MachHide",
title = "Weighted Sums with Two Parameters of Multiple Zeta
Values and Their Formulas",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1903--1921",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501084",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501084",
abstract = "A typical formula of multiple zeta values is the {\em
sum formula\/} which expresses a Riemann zeta value as
a sum of all multiple zeta values of fixed weight and
depth. Recently {\em weighted sum formulas\/}, which
are weighted analogues of the sum formula, have been
studied by many people. In this paper, we give two
formulas of weighted sums with two parameters of
multiple zeta values. As applications of the formulas,
we find some linear combinations of multiple zeta
values which can be expressed as polynomials of usual
zeta values with coefficients in the rational
polynomial ring generated by the two parameters, and
obtain some identities for weighted sums of multiple
zeta values.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Molteni:2012:RPS,
author = "G. Molteni",
title = "Representation of a $2$-power as sum of $k$
$2$-powers: the asymptotic behavior",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1923--1963",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501096",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501096",
abstract = "A $k$-representation of an integer $ \ell $ is a
representation of \ell as sum of $k$ powers of $2$,
where representations differing by the order are
considered as distinct. Let $ \mathcal {W}(\sigma, k)$
be the maximum number of such representations for
integers $ \ell $ whose binary representation has
exactly $ \sigma $ non-zero digits. $ \mathcal
{W}(\sigma, k)$ can be recovered from via an explicit
formula, thus in some sense is the fundamental object.
In this paper we prove that $ (\mathcal {W}(1, k) /
k!)^{1 / k}$ tends to a computable limit as $k$
diverges. This result improves previous bounds which
were obtained with purely combinatorial tools.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Girstmair:2012:DSS,
author = "Kurt Girstmair",
title = "{Dedekind} Sums with Small Denominators",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1965--1970",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501102",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501102",
abstract = "Let (m, n) = 1 and S(m/n) = 12s(m/n), where s(m/n) is
the usual Dedekind sum. Then. Let q \geq 1 be a divisor
of n. We give a necessary and sufficient condition for
and, thereby, generalize a result of Rademacher that
concerns the case q = 1. Further, we study the
structure of possible denominators q of S(m/n).
Finally, we show that for certain quadratic irrationals
of odd period length l the convergents s$_k$ /t$_k$, k
\equiv l - 1 (mod 2l), yield stationary values of
S(s$_k$ /t$_k$). This means that, for large values of
k, the denominators q of these Dedekind sums are very
small compared with t$_k$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Wakabayashi:2012:HRM,
author = "Noriko Wakabayashi",
title = "On {Hoffman}'s Relation for Multiple Zeta-Star
Values",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1971--1976",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501114",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501114",
abstract = "The multiple zeta values are natural generalization of
Riemann zeta values, which are real numbers first
considered by Euler. It is known that there are many
linear relations among these values with rational
coefficients. Hoffman [Multiple harmonic series, {\em
Pacific J. Math.\/} 152 (1992) 275--290] gives a class
of relations among multiple zeta values, which is
called Hoffman's relation. In this paper, we show the
corresponding relation for multiple zeta-star values by
using partial-fractions expansion as Hoffman did.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Liu:2012:SIR,
author = "Zhi-Guo Liu",
title = "Some Inverse Relations and Theta Function Identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "1977--2002",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501126",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501126",
abstract = "Two pairs of inverse relations for elliptic theta
functions are established with the method of Fourier
series expansion, which allow us to recover many
classical results in theta functions. Many nontrivial
new theta function identities are discovered. Some
curious trigonometric identities are derived.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Guo:2012:NCS,
author = "Victor J. W. Guo and Jiang Zeng",
title = "New Congruences for Sums Involving {Ap{\'e}ry} Numbers
Or Central {Delannoy} Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2003--2016",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501138",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501138",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Broughan:2012:SPB,
author = "Kevin A. Broughan",
title = "On Shifted Primes and Balanced Primes",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2017--2033",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S179304211250114X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250114X",
abstract = "The asymptotic order of the number of primes, which
are such that the shift by a fixed integer is a number
supported by a given set of primes times a coprime
squarefree number, is determined. The order is also
determined when the shift and its negative have this
same shape. In each case the order is dependent only on
the set of primes and the squarefree core of the
shift.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Miyazaki:2012:DE,
author = "T. Miyazaki and A. Togb{\'e}",
title = "The {Diophantine} equation $ (2 a m - 1)^x + (2 m)^y =
(2 a m + 1)^z $",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2035--2044",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501151",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501151",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ayad:2012:RPU,
author = "Mohamed Ayad and Omar Kihel",
title = "Recognizing the Primes Using Permutations",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2045--2057",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501163",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501163",
abstract = "Let n \geq 3 be an integer. For any permutation \sigma
of A = {0, 1, \ldots, n-1}, set. It is proved that n is
prime if and only if {\u{3}008}\sigma, n{\u{3}009}
\equiv 0 (mod n) for any \sigma . When n is composite,
we show that there exist cycles of any length
satisfying this congruence. We show as well that the
analog statement is true for cycles of length at least
2 not satisfying the congruence.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Meher:2012:SRR,
author = "Jaban Meher",
title = "Some Remarks on {Rankin--Cohen} Brackets of
Eigenforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2059--2068",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501175",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501175",
abstract = "We investigate the cases for which products of two
quasimodular or nearly holomorphic eigenforms are
eigenforms. We also generalize the results of Ghate [On
products of eigenforms, {\em Acta Arith.\/} 102 (2002)
27--44] to the case of Rankin--Cohen brackets.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alkan:2012:RSB,
author = "Emre Alkan",
title = "{Ramanujan} Sums and the {Burgess} Zeta Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2069--2092",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112501187",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501187",
abstract = "The Mellin transform of a summatory function involving
weighted averages of Ramanujan sums is obtained in
terms of Bernoulli numbers and values of the Burgess
zeta function. The possible singularity of the Burgess
zeta function at s = 1 is then shown to be equivalent
to the evaluation of a certain infinite series
involving such weighted averages. Bounds on the size of
the tail of these series are given and specific bounds
are shown to be equivalent to the Riemann hypothesis.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anonymous:2012:AIV,
author = "Anonymous",
title = "Author Index (Volume 8)",
journal = j-INT-J-NUMBER-THEORY,
volume = "8",
number = "8",
pages = "2093--2098",
month = dec,
year = "2012",
DOI = "https://doi.org/10.1142/S1793042112990011",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112990011",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Das:2013:NPS,
author = "Soumya Das and Satadal Ganguly",
title = "Nonvanishing of {Poincar{\'e}} Series on Average",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "1--8",
month = feb,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112501205",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501205",
abstract = "We show that a positive proportion of the Poincar{\'e}
series do not vanish identically when either the index
or the weight varies over an interval of suitable
length, the other one being fixed.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Das:2013:NDE,
author = "Soumya Das",
title = "On the Natural Densities of Eigenvalues of a {Siegel}
Cusp Form of Degree 2",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "9--15",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501217",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501217",
abstract = "We prove explicit lower bounds for the density of the
sets of primes p such that eigenvalues \lambda$_p$ of a
Siegel cusp form of degree 2 satisfy c$_2$ >
\lambda$_p$ > c$_1$, for c$_1$, c$_2$ real. A similar
result is also proved for the set of primes such that
\mid \lambda$_p$ \mid > c.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2013:TCN,
author = "Tsz Ho Chan",
title = "Twin Cubefull Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "17--26",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501229",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501229",
abstract = "A number is cubefull if the exponent of every prime in
its prime factorization is at least three. In this
paper, we give, for a fixed l, the number of pairs of
cubefull numbers n, n + l such that n is less than a
given quantity.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hashimoto:2013:AFC,
author = "Yasufumi Hashimoto",
title = "Asymptotic Formulas for Class Number Sums of
Indefinite Binary Quadratic Forms on Arithmetic
Progressions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "27--51",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501230",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501230",
abstract = "It is known that there is a one-to-one correspondence
between equivalence classes of primitive indefinite
binary quadratic forms and primitive hyperbolic
conjugacy classes of the modular group. Due to such a
correspondence, Sarnak obtained the asymptotic formula
for the class number sum in order of the fundamental
unit by using the prime geodesic theorem for the
modular group. In the present paper, we propose
asymptotic formulas of the class number sums over
discriminants on arithmetic progressions. Since there
are relations between the arithmetic properties of the
discriminants and the conjugacy classes in the finite
groups given by the modular group and its congruence
subgroups, we can get the desired asymptotic formulas
by arranging the Tchebotarev-type prime geodesic
theorem. While such asymptotic formulas were already
given by Raulf, the approaches are quite different, the
expressions of the leading terms of our asymptotic
formulas are simpler and the estimates of the remainder
terms are sharper.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gunnells:2013:MFE,
author = "Paul E. Gunnells and Dan Yasaki",
title = "Modular Forms and Elliptic Curves Over the Cubic Field
of Discriminant $ - 23 $",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "53--76",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501242",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501242",
abstract = "Let F be the cubic field of discriminant --23 and let
be its ring of integers. By explicitly computing
cohomology of congruence subgroups of, we
computationally investigate modularity of elliptic
curves over F.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dickinson:2013:MTM,
author = "Detta Dickinson and Mumtaz Hussain",
title = "The Metric Theory of Mixed Type Linear Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "77--90",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501278",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501278",
abstract = "In this paper the metric theory of Diophantine
approximation of linear forms that are of mixed type is
investigated. Khintchine--Groshev theorems are
established together with the Hausdorff measure
generalizations. The latter includes the original
dimension results obtained in [H. Dickinson, The
Hausdorff dimension of sets arising in metric
Diophantine approximation, {\em Acta Arith.\/} 68(2)
(1994) 133--140] as special cases.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chen:2013:MGR,
author = "Imin Chen and Ian Kiming and Gabor Wiese",
title = "On Modular {Galois} Representations Modulo Prime
Powers",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "91--113",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501254",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501254",
abstract = "We study modular Galois representations $ \bmod p^m $.
We show that there are three progressively weaker
notions of modularity for a Galois representation $
\bmod p^m $: We have named these ``strongly'',
``weakly'', and ``dc-weakly'' modular. Here, ``dc''
stands for ``divided congruence'' in the sense of Katz
and Hida. These notions of modularity are relative to a
fixed level M. Using results of Hida we display a
level-lowering result (``stripping-of-powers of $p$
away from the level''): a $ \bmod p^m$ strongly modular
representation of some level $ N_{p^r}$ is always
dc-weakly modular of level $N$ (here, $N$ is a natural
number not divisible by $p$). We also study eigenforms
$ \bmod p^m$ corresponding to the above three notions.
Assuming residual irreducibility, we utilize a theorem
of Carayol to show that one can attach a Galois
representation mod pm to any ``dc-weak'' eigenform, and
hence to any eigenform mod pm in any of the three
senses. We show that the three notions of modularity
coincide when $ m = 1$ (as well as in other particular
cases), but not in general.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Anavi:2013:CF,
author = "Aria Anavi and Paul Pollack and Carl Pomerance",
title = "On congruences of the form $ \sigma (n) \equiv a
(\bmod n) $",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "115--124",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501266",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501266",
abstract = "We study the distribution of solutions n to the
congruence \sigma(n) \equiv a (mod n). After excluding
obvious families of solutions, we show that the number
of these n \leq x is at most x$^{\frac {1}{2} + o(1)}$,
as x \rightarrow \infty, uniformly for integers a with
\mid a\mid \leq x$^{{\u {0}0bc}}$. As a concrete
example, the number of composite solutions n \leq x to
the congruence \sigma(n) \equiv 1 (mod n) is at most
x$^{\frac {1}{2} + o(1)}$. These results are analogues
of theorems established for the Euler \varphi -function
by the third-named author.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{McLeman:2013:CNI,
author = "Cam McLeman and Dustin Moody",
title = "Class Numbers Via $3$-Isogenies and Elliptic
Surfaces",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "125--137",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211250128X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250128X",
abstract = "We show that a character sum attached to a family of
3-isogenies defined on the fibers of a certain elliptic
surface over {$ \mathbb {F} $}$_p$ relates to the class
number of the quadratic imaginary number field. In this
sense, this provides a higher-dimensional analog of
some recent class number formulas associated to
2-isogenies of elliptic curves.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Fukshansky:2013:WRI,
author = "Lenny Fukshansky and Glenn Henshaw and Philip Liao and
Matthew Prince and Xun Sun and Samuel Whitehead",
title = "On Well-Rounded Ideal Lattices {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "139--154",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501291",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501291",
abstract = "We study well-rounded lattices which come from ideals
in quadratic number fields, generalizing some recent
results of the first author with Petersen [On ideal
well-Rounded lattices, {\em Int. J. Number Theory\/}
8(1) (2002) 189--206]. In particular, we give a
characterization of ideal well-rounded lattices in the
plane and show that a positive proportion of real and
imaginary quadratic number fields contains ideals
giving rise to well-rounded lattices.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Laurincikas:2013:UHZ,
author = "Antanas Laurin{\v{c}}ikas",
title = "On the Universality of the {Hurwitz} Zeta-Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "155--165",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501308",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501308",
abstract = "It is known that the Hurwitz zeta-function \zeta (s,
\alpha) with transcendental or rational parameter
\alpha is universal in the sense that its shifts \zeta
(s + i\tau, \alpha), \tau \in {\mathbb{R}}, approximate
with a given accuracy any analytic function uniformly
on compact subsets of the strip D = {s \in {\mathbb{C}}
: \frac{1}{2} < \sigma < 1}. Let H(D) denote the space
of analytic functions on D equipped with the topology
of uniform convergence on compacta. In the paper, the
classes of functions F : H(D) \rightarrow H(D) such
that F(\zeta (s, \alpha)) is universal in the above
sense are considered. For example, if F is continuous
and, for each polynomial p = p(s), the set F$^{-1}$ {p}
is non-empty, then F(\zeta (s, \alpha)) with
transcendental \alpha is universal.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cho:2013:SZM,
author = "Peter Jaehyun Cho",
title = "Simple Zeros of {Maass} {$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "167--178",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211250131X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250131X",
abstract = "We show that one simple zero of a Maass {$L$}-function
implies infinitely many simple zeros of the
{$L$}-function. Since Str{\"o}mbergsson found simple
zeros of three different even Maass {$L$}-functions, we
know that there are at least three Maass
{$L$}-functions having infinitely many simple zeros.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Shahverdian:2013:EFD,
author = "Ashot Shahverdian and Adem Kilicman",
title = "Exact formula for distribution of sequences $ \{
\omega n \} $",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "179--187",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501321",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501321",
abstract = "An exact formula for distribution of sequences of
fractional parts is proved. This provides us with a
possibility for computational study of their
discrepancies by the means of integer-number
programming.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Xia:2013:RIC,
author = "Ernest X. W. Xia and Olivia X. M. Yao",
title = "On the Representations of Integers by Certain
Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "189--204",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501333",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501333",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kasten:2013:CVR,
author = "Hendrik Kasten and Claus-G{\"u}nther Schmidt",
title = "The Critical Values of {Rankin--Selberg}
Convolutions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "1",
pages = "205--256",
month = feb,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501345",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501345",
abstract = "For a pair (\pi, \sigma) of cuspidal automorphic
representations of GL$_n$ and GL$_{n - 1}$, both of
non-vanishing cohomology, we show algebraicity
properties of critical values of the associated
Rankin--Selberg {$L$}-function twisted by finite-order
characters. A certain non-vanishing assumption about
the associated archimedean Rankin--Selberg pairings on
the cohomology is established for n = 3.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Barth:2013:ITO,
author = "Peter Barth",
title = "{Iwasawa} Theory for One-Parameter Families of
Motives",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "257--319",
month = mar,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112501357",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501357",
abstract = "In [A formulation of conjectures on $p$-adic zeta
functions in non-commutative Iwasawa theory, in {\em
Proc. St. Petersburg Mathematical Society\/}, Vol. 12,
American Mathematical Society Translations, Series 2,
Vol. 219 (American Mathematical Society, Providence,
RI, 2006), pp. 1--85] Fukaya and Kato presented
equivariant Tamagawa number conjectures that implied a
very general (non-commutative) Iwasawa main conjecture
for rather general motives. In this article we apply
their methods to the case of one-parameter families of
motives to derive a main conjecture for such families.
On our way there we get some unconditional results on
the variation of the (algebraic) \lambda - and \mu
-invariant. We focus on the results dealing with Selmer
complexes instead of the more classical notion of
Selmer groups. However, where possible we give the
connection to the classical notions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Belaghi:2013:BMT,
author = "Mahmoud Jafari Shah Belaghi and Sergey Khrushchev and
Agamirza E. Bashirov",
title = "On {Bauer--Muir} Transform of Continued Fractions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "321--332",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501369",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501369",
abstract = "In this paper a convergence theorem for continued
fractions with negative parameters is proved. We define
a transformation of a certain kind of continued
fractions to the same kind of continued fractions. This
transformation is obtained by multiple application of
the Bauer--Muir transform and then using the limiting
process. It is shown that a double application of this
transformation is the identity transformation.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zorin:2013:ZOE,
author = "Evgeniy Zorin",
title = "Zero Order Estimates for Analytic Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "333--392",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501370",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:01:30 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501370",
abstract = "In this article we develop an important tool in
transcendental number theory. More precisely, we study
multiplicity estimates (or {\em multiplicity lemmas\/})
for analytic functions. Our main theorem reduces
multiplicity estimates at zero to the study of ideals
in polynomial ring stable under an appropriate map. In
particular, in the case of algebraic morphisms this
result gives a new link between the theory of polarized
algebraic dynamical systems and transcendental number
theory. Specialized to the case of differential
operators this theorem improves Nesterenko's
conditional result on solutions of systems of
differential equations. We also deduce an analog of
Nesterenko's theorem for Mahler's functions and for
solutions of q-difference equations. Further, analyzing
stable ideals we prove the unconditional optimal result
in the case of linear functional systems of generalized
Mahler's type. The latter result generalizes a famous
theorem of Nishioka (1986) previously conjectured by
Mahler (1969). This new multiplicity estimate allows to
prove new results on algebraic independence and on
measures of algebraic independence, as done in Zorin
(2010 and 2011).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Prasad:2013:NPL,
author = "K. C. Prasad and Hrishikesh Mahato and Sudhir Mishra",
title = "A New Point in {Lagrange} Spectrum",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "393--403",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501382",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 11:25:53 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501382",
abstract = "Let $I$ denote the set of all irrational numbers, $
\theta \in I$, and simple continued fraction expansion
of $ \theta $ be $ [a_0, a_1, \ldots, a_n, \ldots]$.
Then $ a_0$ is an integer and $ \{ a_n \}_{n \geq 1}$
is an infinite sequence of positive integers. Let $ M_n
(\theta) = [0, a_n, a_{n - 1}, \ldots, a_1] + [a_{n +
1}, a_{n + 2}, \ldots]$. Then the set of numbers $ \lim
\sup M_n (\theta) \mid \theta \in I$ is called the
Lagrange Spectrum $ \{ \mathfrak {L} \} $. Notably $3$
is the first cluster point of $ \{ \mathfrak {L} \} $.
Essentially $ \lim \inf \mathfrak {L}$ or $ \underbar
{\mathcal {L}} = 3$. Perron [{\"U}ber die approximation
irrationaler Zahlen durch rationale, I, {\em S.-B.
Heidelberg Akad. Wiss., Abh}. {\bf 4} (1921) 17 pp;
{\"U}ber die approximation irrationaler Zahlen durch
rationale, II, {\em S.-B. Heidelberg Akad. Wiss.,
Abh.\/} {\bf 8} (1921) 12 pp.] has found that $ \lim
\inf \lim \sup M_n (\theta) \mid \theta = [a_0, a_1,
a_2, \ldots, a_n, \ldots]$ and $ a_n \geq 3$
frequently. This article forwards the value of $ \lim
\inf \lim s u p M_n (\theta) \mid \theta = [a_0, a_1,
\ldots, a_n, \ldots]$ and $ a_n \geq 4$ frequently, a
long awaited cluster point of Lagrange Spectrum.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pazuki:2013:PMB,
author = "F. Pazuki",
title = "Polarized Morphisms Between {Abelian} Varieties",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "405--411",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501394",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501394",
abstract = "In this paper, we will study the dynamical
Manin--Mumford problem, focusing on the question of
polarizability for endomorphisms of an abelian variety
A and on the action of a Frobenius and its Verschiebung
on the diagonal subvariety of A $ \times $ A. We
complete the study with different polarizability
criteria.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sun:2013:ESC,
author = "Zhi-Hong Sun and Lin-Lin Wang",
title = "An Extension of {Stern}'s Congruence",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "413--419",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501400",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501400",
abstract = "Let {$ E_n $ } be the Euler numbers. In the paper we
determine $ E_{2^m k + b} - E_b $ modulo $ 2^{m + 7} $,
where $k$ and $m$ are positive integers and $ b \in \{
0, 2, 4, \ldots \} $.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Thompson:2013:D,
author = "Lola Thompson",
title = "On the divisors of $ x^n - 1 $ in {$ \mathbb {F}_p[x]
$}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "421--430",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501412",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501412",
abstract = "In a recent paper, we considered integers n for which
the polynomial x$^n$-- 1 has a divisor in
{\mathbb{Z}}[x] of every degree up to n, and we gave
upper and lower bounds for their distribution. In this
paper, we consider those n for which the polynomial
x$^n$-- 1 has a divisor in {$ \mathbb {F} $}$_p$ [x] of
every degree up to n, where p is a rational prime.
Assuming the validity of the Generalized Riemann
Hypothesis, we show that such integers n have
asymptotic density 0.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Zhang:2013:MVI,
author = "Deyu Zhang and Meimei L{\"u} and Wenguang Zhai",
title = "On the Mean Value of the Index of Composition of an
Integer {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "431--445",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501424",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501424",
abstract = "For each integer n \geq 2, let be the index of
composition of n, where \gamma (n) \coloneq \prod$_{p
\mid n}$ p. The index of composition of an integer
measures the multiplicity of its prime factors. In this
paper, we obtain a new asymptotic formula of the sum $
\sum_{n \leq x}$ \lambda$^{-k}$ (n). Furthermore, we
improve the error term under the Riemann Hypothesis.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Clark:2013:TPE,
author = "Pete L. Clark and Brian Cook and James Stankewicz",
title = "Torsion Points on Elliptic Curves with Complex
Multiplication (with an Appendix by {Alex Rice})",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "447--479",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501436",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501436",
abstract = "We present seven theorems on the structure of prime
order torsion points on CM elliptic curves defined over
number fields. The first three results refine bounds of
Silverberg and Prasad--Yogananda by taking into account
the class number of the CM order and the splitting of
the prime in the CM field. In many cases we can show
that our refined bounds are optimal or asymptotically
optimal. We also derive asymptotic upper and lower
bounds on the least degree of a CM-point on X$_1$ (N).
Upon comparison to bounds for the least degree for
which there exist infinitely many rational points on
X$_1$ (N), we deduce that, for sufficiently large N,
X$_1$ (N) will have a rational CM point of degree
smaller than the degrees of at least all but finitely
many non-CM points.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Browning:2013:IKS,
author = "T. D. Browning and A. Haynes",
title = "Incomplete {Kloosterman} Sums and Multiplicative
Inverses in Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "481--486",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501448",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501448",
abstract = "We investigate the solubility of the congruence xy
\equiv 1 (mod p), where p is a prime and x, y are
restricted to lie in suitable short intervals. Our work
relies on a mean value theorem for incomplete
Kloosterman sums.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Yao:2013:EFF,
author = "Olivia X. M. Yao and Ernest X. W. Xia and J. Jin",
title = "Explicit Formulas for the {Fourier} Coefficients of a
Class of Eta Quotients",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "487--503",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211250145X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250145X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kokluce:2013:RNTa,
author = "B{\"u}lent K{\"o}kl{\"u}ce",
title = "The Representation Numbers of Three Octonary Quadratic
Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "505--516",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501461",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501461",
abstract = "In this study we use some known convolution sums to
find the representation number for each of the three
octonary quadratic forms, and.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Richard:2013:RGC,
author = "Rodolphe Richard",
title = "R{\'e}partition galoisienne d'une classe
d'isog{\'e}nie de courbes elliptiques. ({French})
[{Galois} distribution of an isogeny class of elliptic
curves]",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "2",
pages = "517--543",
month = mar,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501199",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:14:38 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501199",
abstract = "Dans cet article, on montre que les orbites sous
Galois des invariants modulaires associ{\'e}s {\`a} des
courbes elliptiques complexes {\em sans multiplication
complexe\/} variant dans {\em une m{\^e}me classe
d'isog{\'e}nie\/} s'{\'e}quidistribuent dans la courbe
modulaire vers la probabilit{\'e} hyperbolique. La
d{\'e}monstration repose sur des arguments de
th{\'e}orie ergodique, notamment le {\em
th{\'e}or{\`e}me de Ratner\/} (cf. [A. Eskin et H. Oh,
Ergodic theoretic proof of equidistribution of Hecke
points, {\em Ergodic Theory Dynam. Systems\/} 26(1)
(2006) 163--167]), ainsi que sur le {\em
th{\'e}or{\`e}me de l'image ouverte de Serre\/} [J.-P.
Serre, {\em Abelian l-Adic Representations and Elliptic
Curves\/} (W. A. Benjamin, New York, 1968);
Propri{\'e}t{\'e}s Galoisiennes des points d'ordre fini
des courbes elliptiques, {\em Invent. Math.\/} 15(4)
(1972) 259--331] dans le cas o{\`u} les invariants
modulaires consid{\'e}r{\'e}s sont alg{\'e}briques sur
Q, et des r{\'e}sultats de G. Shimura dans le cas
transcendant [ {\em Introduction to the Arithmetic
Theory of Automorphic Functions\/}, Publications of the
Mathematical Society of Japan (Princeton University
Press, Princeton, NJ, 1994)]. In this article, it is
shown that Galois orbits of invariants associated with
{\em non-CM\/} and {\em pairwise isogenous\/} complex
elliptic curves equidistribute in the classical modular
curve towards the hyperbolic probability measure. The
proof is based on arguments from ergodic theory,
especially {\em Ratner's theorem on unipotent flows\/}
(cf. [A. Eskin and H. Oh, Ergodic theoretic proof of
equidistribution of Hecke points, {\em Ergodic Theory
Dynam. Systems\/} 26(1) (2006) 163--167]), as well as
on {\em Serre's open image theorem\/} [J.-P. Serre,
{\em Abelian l-Adic Representations and Elliptic
Curves\/} (W. A. Benjamin, New York, 1968);
Propri{\'e}t{\'e}s Galoisiennes des points d'ordre fini
des courbes elliptiques, {\em Invent. Math.\/} 15(4)
(1972) 259--331] in case of algebraic invariants, and
on G. Shimura's work in the transcendant case [ {\em
Introduction to the Arithmetic Theory of Automorphic
Functions\/}, Publications of the Mathematical Society
of Japan (Princeton University Press, Princeton, NJ,
1994)].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
language = "French",
}
@Article{Komatsu:2013:HCN,
author = "Takao Komatsu",
title = "Hypergeometric {Cauchy} Numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "545--560",
month = may,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042112501473",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501473",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mourtada:2013:OT,
author = "M. Mourtada and V. Kumar Murty",
title = "{Omega} Theorems For {$ \frac {L'}{L}(1, \chi_D) $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "561--581",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501485",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501485",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ulas:2013:NES,
author = "Maciej Ulas and Andrzej Schinzel",
title = "A Note on {Erd{\H{o}}s--Straus} and
{Erd{\H{o}}s--Graham} Divisibility Problems (with an
Appendix by {Andrzej Schinzel})",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "583--599",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501497",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501497",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Mei:2013:APS,
author = "Shu-Yuan Mei and Yong-Gao Chen",
title = "Arithmetic Progressions in Sumsets and Difference
Sets",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "601--606",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501503",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501503",
abstract = "Let s \geq 1, A$_i$ \subseteq {1,2,\ldots, N} (1 \leq
i \leq s) and k \geq 3 be an odd integer. In this
paper, one of the main results is: if, then (a) each of
A$_i$- A$_j$ (1 \leq i, j \leq s) contains an
arithmetic progression of length k with the same common
difference; (b) all sets A$_i$- A$_i$ (1 \leq i \leq s)
contain a common arithmetic progression of length k.
Finally, we pose several problems for further
research.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Keil:2013:MEE,
author = "Eugen Keil",
title = "Moment estimates for exponential sums over $k$-free
numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "607--619",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501515",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501515",
abstract = "We investigate the size of L$^p$-integrals for
exponential sums over k-free numbers and prove
essentially tight bounds.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Djankovic:2013:EHP,
author = "Goran Djankovi{\'c}",
title = "{Euler--Hadamard} Products and Power Moments of
Symmetric Square {$L$}-Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "621--639",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501527",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501527",
abstract = "In this paper we prove asymptotic formulas for general
moments of partial Euler products and the first and the
second moments of partial Hadamard products related to
central values of the family of {$L$}-functions
associated to the symmetric square lifts of holomorphic
modular forms for SL$_2$ ({\mathbb{Z}}). Then using a
hybrid Euler--Hadamard product formula for the central
value, we relate these results with conjectures for
general power moments of {$L$}-functions in this family
and with Random Matrix Theory interpretations. This
continues the work done previously by
Gonek--Hughes--Keating and Bui--Keating for other
families of {$L$}-functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Dewar:2013:AFC,
author = "Michael Dewar and M. Ram Murty",
title = "An asymptotic formula for the coefficients of $ j(z)
$",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "641--652",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501539",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501539",
abstract = "We obtain a new proof of an asymptotic formula for the
coefficients of the j-invariant of elliptic curves. Our
proof does not use the circle method. We use Laplace's
method of steepest descent and the Hardy--Ramanujan
asymptotic formula for the partition function. (The
latter asymptotic formula can be derived without the
circle method.)",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Cerri:2013:ETD,
author = "Jean-Paul Cerri and J{\'e}r{\^o}me Chaubert and Pierre
Lezowski",
title = "{Euclidean} Totally Definite Quaternion Fields Over
the Rational Field and Over Quadratic Number Fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "653--673",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501540",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501540",
abstract = "In this paper we study totally definite quaternion
fields over the rational field and over quadratic
number fields. We establish a complete list of all such
fields which are Euclidean. Moreover, we prove that
every field in this list is in fact norm-Euclidean. The
proofs are both theoretical and algorithmic.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Waldherr:2013:AMH,
author = "Matthias Waldherr",
title = "Asymptotics for Moments of Higher Ranks",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "675--712",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501552",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501552",
abstract = "Bringmann, Mahlburg, and Rhoades have found asymptotic
expressions for all moments of the partition statistics
rank and crank. In this work we extend their methods to
higher ranks. The T-rank, introduced by Garvan, for odd
integers T = 3 is a natural generalization of the rank
(T = 3) and crank (T = 1).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Andersen:2013:HTC,
author = "Nickolas Andersen",
title = "{Hecke}-Type Congruences for Two Smallest Parts
Functions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "713--728",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501564",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501564",
abstract = "We prove infinitely many congruences modulo 3, 5, and
powers of 2 for the overpartition function and two
smallest parts functions: for overpartitions and
M2spt(n) for partitions without repeated odd parts.
These resemble the Hecke-type congruences found by
Atkin for the partition function p(n) in 1966 and
Garvan for the smallest parts function spt(n) in 2010.
The proofs depend on congruences between the generating
functions for, , and M2spt({\em n\/}) and eigenforms
for the half-integral weight Hecke operator
T(\ell$^2$).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chojecki:2013:DCP,
author = "Przemyslaw Chojecki",
title = "Density of Crystalline Points on Unitary {Shimura}
Varieties",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "729--744",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501576",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501576",
abstract = "We prove that crystalline points are dense in the
spectrum of the completed Hecke algebra on unitary
Shimura varieties.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Miller:2013:WBR,
author = "Lance Edward Miller",
title = "A {Witt--Burnside} ring attached to a pro-dihedral
group",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "745--757",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501588",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501588",
abstract = "The ring of $p$-typical Witt vectors is an
indispensable tool in number theory and mixed
characteristic commutative algebra. Witt vectors were
significantly generalized by Dress and Siebeneicher by
producing for any profinite group $G$, a ring-valued
functor $ W_G$. The $p$-typical Witt vectors are
recovered as the example $ G = Z_p$. This paper
explores the structure of the ring $ W_{D 2^\infty
}(k)$ where $k$ is a field of characteristic $2$ and $
D_{2^\infty }(k) \coloneq \lim D_{2^n}$ [under left
arrow].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Borwein:2013:NBP,
author = "Peter Borwein and Tam{\'a}s Erd{\'e}lyi",
title = "A Note on {Barker} Polynomials",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "759--767",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211250159X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250159X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hussain:2013:MRS,
author = "M. Hussain and S. Kristensen",
title = "Metrical Results on Systems of Small Linear Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "769--782",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501606",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501606",
abstract = "In this paper the metric theory of Diophantine
approximation associated with the small linear forms is
investigated. Khintchine--Groshev theorems are
established along with Hausdorff measure generalization
without the monotonic assumption on the approximation
function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Li:2013:SIH,
author = "Zhong-Hua Li",
title = "Some Identities in the Harmonic Algebra Concerned with
Multiple Zeta Values",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "783--798",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042112501618",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042112501618",
abstract = "Let {$ \mathfrak {A} $} be a commutative {$ \mathbb
{Q} $}-algebra, A be an alphabet of non-commutative
letters and {$ \mathfrak {h} $}$^1$ be the
non-commutative polynomial algebra generated by the set
A over the algebra {$ \mathfrak {A} $}. The harmonic
algebra {$ \mathfrak {h} $}$^1$ is closely related to
multiple zeta values and multiple zeta-star values in
some special case. Some identities in the algebra {$
\mathfrak {h} $}$^1$ are given.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ramakrishnan:2013:ECS,
author = "B. Ramakrishnan and Brundaban Sahu",
title = "Evaluation of the convolution sums $ \sum_{l + 15 m =
n} \sigma (l) \sigma (m) $ and $ \sum_{3l + 5m = n}
\sigma (l) \sigma (m) $ and an application",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "799--809",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211250162X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211250162X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chen:2013:ECP,
author = "Yong-Gao Chen and Jing-Rui Lou",
title = "Erratum: {``The congruent properties for $ r_s(n)
$''}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "3",
pages = "811--811",
month = may,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113920012",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
note = "See \cite{Chen:2011:CP}.",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113920012",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Martin:2013:NVD,
author = "Greg Martin and Nathan Ng",
title = "Nonzero Values of {Dirichlet} {$L$}-Functions in
Vertical Arithmetic Progressions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "813--843",
month = jun,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042113500140",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500140",
abstract = "Let L(s, \chi) be a fixed Dirichlet {$L$}-function.
Given a vertical arithmetic progression of T points on
the line {\mathfrak{R}}s = \frac{1}{2}, we show that at
least cT/log T of them are not zeros of L(s, \chi) (for
some positive constant c). This result provides some
theoretical evidence towards the conjecture that all
nonnegative ordinates of zeros of Dirichlet
{$L$}-functions are linearly independent over the
rationals. We also establish an upper bound (depending
upon the progression) for the first member of the
arithmetic progression that is not a zero of L(s,
\chi).",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Li:2013:MZS,
author = "Yuanlin Li and Jiangtao Peng",
title = "Minimal Zero-Sum Sequences of Length Four Over Finite
Cyclic Groups {II}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "845--866",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500012",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500012",
abstract = "Let G be a finite cyclic group. Every sequence S over
G can be written in the form S = (n$_1$ g)\cdot \ldots
\cdot (n$_l$ g) where g \in G and n$_1$, \ldots, n$_l$
\in [1, ord(g)], and the index ind(S) of S is defined
to be the minimum of (n$_1$ +\cdots +n$_l$)/ord(g) over
all possible g \in G such that {\u{3}008}g{\u{3}009} =
G. An open problem on the index of length four
sequences asks whether or not every minimal zero-sum
sequence of length 4 over a finite cyclic group G with
gcd(|G|, 6) = 1 has index 1. In this paper, we show
that if G = {\u{3}008}g{\u{3}009} is a cyclic group
with order of a product of two prime powers and
gcd(|G|, 6) = 1, then every minimal zero-sum sequence S
of the form S = (g)(n$_2$ g)(n$_3$ g)(n$_4$ g) has
index 1. In particular, our result confirms that the
above problem has an affirmative answer when the order
of G is a product of two different prime numbers or a
prime power, extending a recent result by the first
author, Plyley, Yuan and Zeng.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Reynya:2013:SHD,
author = "M. A. Reynya",
title = "Symmetric Homogeneous {Diophantine} Equations of Odd
Degree",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "867--876",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500024",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500024",
abstract = "An elementary approach for finding non-trivial
parametric solutions to homogeneous symmetric
Diophantine equations of odd degree in sufficiently
many variables is presented. The method is based on
studying a model case of quintic symmetric Diophantine
equations in six variables. We prove that every
symmetric form of odd degree n \geq 5 in 6 \cdot 2$^{n
- 5}$ variables has a rational parametric solution
depending on 2n-8 parameters. We also present a
solution to a problem of Waring type: if F(x$_1$,
\ldots, x$_N$) is a symmetric form of odd degree n \geq
5 in N = 6 \cdot 2$^{n - 4}$ variables, then for any q
\in {$ \mathbb {Q}$} the equation F(x$_i$) = q has a
rational parametric solution depending on 2n - 6
parameters.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Baier:2013:MIS,
author = "S. Baier",
title = "Multiplicative Inverses in Short Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "877--884",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500036",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500036",
abstract = "We give an alternative proof of a recent result by T.
D. Browning and A. Haynes (arXiv:1204.6374v1) on
multiplicative inverses in sequences of intervals and
improve this result under additional conditions on the
spacing of these intervals.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chan:2013:SNA,
author = "Tsz Ho Chan and Kai Man Tsang",
title = "Squarefull Numbers in Arithmetic Progressions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "885--901",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500048",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500048",
abstract = "In this paper, we study squarefull numbers in
arithmetic progressions. We find the least such
squarefull number by Dirichlet's hyperbola method as
well as Burgess bound on character sums. We also obtain
a best possible almost all result via a large sieve
inequality of Heath-Brown on real characters.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hu:2013:DID,
author = "Yong Hu",
title = "On the Distribution of Integers with Divisors in Two
Consecutive Intervals",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "903--915",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211350005X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211350005X",
abstract = "We investigate a new problem related to the
multiplicative structure of integers. We introduce a
new function H$_{1, 1}$ (x, y, z$_1$, z$_2$), the
number of positive integers n \leq x having exactly one
divisor in interval (y, z$_1$ ] and one in (z$_1$,
z$_2$ ]. Our aim is to estimate its order of magnitude
under some general conditions on y, z$_1$ and z$_2$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ramakrishnan:2013:CBJ,
author = "B. Ramakrishnan and Karam Deo Shankhadhar",
title = "On a Correspondence Between {Jacobi} Cusp Forms and
Elliptic Cusp Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "917--937",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500061",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500061",
abstract = "In this paper, we prove a generalization of a
correspondence between holomorphic Jacobi cusp forms of
higher degree (matrix index) and elliptic cusp forms
obtained by K. Bringmann [Lifting maps from a vector
space of Jacobi cusp forms to a subspace of elliptic
modular forms, {\em Math. Z.\/} 253 (2006) 735--752],
for forms of higher levels (for congruence subgroups).
To achieve this, we make use of the method adopted by
M. Manickam and the first author in Sec. 3 of [On
Shimura, Shintani and Eichler--Zagier correspondences,
{\em Trans. Amer. Math. Soc.\/} 352 (2000) 2601--2617],
who obtained similar correspondence in the degree one
case. We also derive a similar correspondence in the
case of skew-holomorphic Jacobi forms (matrix index and
for congruence subgroups). Such results in the degree
one case (for the full group) were obtained by N.-P.
Skoruppa [Developments in the theory of Jacobi forms,
in {\em Automorphic Functions and Their
Applications\/}, Khabarovsk, 1988 (Acad. Sci. USSR,
Inst. Appl. Math., Khabarovsk, 1990), pp. 168--185;
Binary quadratic forms and the Fourier coefficients of
elliptic and Jacobi modular forms, {\em J. Reine Angew.
Math.\/} 411 (1990) 66--95] and by M. Manickam
[Newforms of half-integral weight and some problems on
modular forms, Ph.D. thesis, University of Madras
(1989)].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Radu:2013:CMS,
author = "Cristian-Silviu Radu and James A. Sellers",
title = "Congruences modulo squares of primes for {Fu}'s $k$
dots bracelet partitions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "939--943",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500073",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500073",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Garunkstis:2013:DMS,
author = "Ram{\=u}nas Garunk{\v{s}}tis and Justas Kalpokas",
title = "The Discrete Mean Square of the {Dirichlet}
{$L$}-Function at Nontrivial Zeros of Another
{Dirichlet} {$L$}-Function",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "945--963",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500085",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500085",
abstract = "We consider the sum of squared absolute values of the
Dirichlet {$L$}-function taken at the nontrivial zeros
of another Dirichlet {$L$}-function.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Sun:2013:CCL,
author = "Zhi-Hong Sun",
title = "Congruences Concerning {Legendre} Polynomials {III}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "965--999",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500097",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500097",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Chu:2013:DIS,
author = "Wenchang Chu",
title = "Derivative Inverse Series Relations and {Lagrange}
Expansion Formula",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "1001--1013",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500103",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500103",
abstract = "A new pair of inverse series relations is established
with the connection coefficients being expressed as
higher derivatives of two fixed analytic functions. As
applications, new proofs for the Lagrange expansion
formulae are presented and Pfaff--Cauchy's
generalizations of the Leibniz rule are reviewed.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bui:2013:TAF,
author = "H. M. Bui",
title = "Twists of Automorphic {$L$}-Functions at the Central
Point",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "1015--1053",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500115",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500115",
abstract = "We study the nonvanishing of twists of automorphic
{$L$}-functions at the center of the critical strip.
Given a primitive character \chi modulo D satisfying
some technical conditions, we prove that the twisted
{$L$}-functions L(f.\chi, s) do not vanish at s =
\frac{1}{2} for a positive proportion of primitive
forms of weight 2 and level q, for large prime q. We
also investigate the central values of high derivatives
of L(f.\chi, s), and from that derive an upper bound
for the average analytic rank of the studied
{$L$}-functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Toh:2013:RFN,
author = "Pee Choon Toh",
title = "On Representations by Figurate Numbers: a Uniform
Approach to the Conjectures of {Melham}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "1055--1071",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500127",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500127",
abstract = "Using known formulas for R$_{(a, b)}$ (n), the number
of representations of n as a times a square plus b
times a square, we prove 21 conjectured formulas of
Melham on the number of representations of n as sums of
triangular, pentagonal and heptagonal numbers. We also
demonstrate how our technique can be used to prove the
other 277 conjectured formulas of Melham concerning
representations by other figurate numbers.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kane:2013:ANS,
author = "Daniel M. Kane",
title = "An Asymptotic for the Number of Solutions to Linear
Equations in Prime Numbers from Specified {Chebotarev}
Classes",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "4",
pages = "1073--1111",
month = jun,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500139",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500139",
abstract = "We extend results relating to Vinogradov's three
primes theorem to provide asymptotic estimates for the
number of solutions to a given linear equation in three
or more prime numbers under the additional constraint
that each of the primes involved satisfies specialized
Chebotarev conditions. In particular, we show that such
solutions can be expected to exist unless a solution
would violate some local constraint.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Pankowski:2013:EVF,
author = "{\l}ukasz Pa{\'n}kowski and J{\"o}rn Steuding",
title = "Extreme Values of {$L$}-Functions from the {Selberg}
Class",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1113--1124",
month = aug,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042113500152",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500152",
abstract = "We prove estimates for extreme values of
{$L$}-functions from the Selberg class under assumption
of the corresponding analogue of the Riemann
hypothesis. The method of proof combines Montgomery's
approach with an effective version of Kronecker's
diophantine approximation theorem due to Weber.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Kokluce:2013:RNC,
author = "B{\"u}lent K{\"o}kl{\"u}ce",
title = "The Representation Numbers of Certain Octonary
Quadratic Forms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1125--1139",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500164",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500164",
abstract = "In this study we derive formulae for the number of
representations of n by the octonary quadratic forms
for any n \in \mathbb{N} $_0$.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Voutier:2013:LCS,
author = "Paul Voutier and Minoru Yabuta",
title = "{Lang}'s conjecture and sharp height estimates for the
elliptic curves $ y^2 = x^3 + a x $",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1141--1170",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500176",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500176",
abstract = "For elliptic curves given by the equation $ E_a $:
y$^2$ = x$^3$ + ax, we establish the best-possible
version of Lang's conjecture on the lower bound for the
canonical height of non-torsion rational points along
with best-possible upper and lower bounds for the
difference between the canonical and logarithmic
height.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Tasaka:2013:SMZ,
author = "Koji Tasaka and Shuji Yamamoto",
title = "On Some Multiple Zeta-Star Values of One-Two-Three
Indices",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1171--1184",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500188",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500188",
abstract = "In this paper, we present some identities for multiple
zeta-star values with indices obtained by inserting 3
or 1 into the string 2, \ldots, 2. Our identities give
analogues of Zagier's evaluation of \zeta (2, \ldots,
2, 3, 2, \ldots, 2) and examples of a kind of duality
of multiple zeta-star values. Moreover, their
generalizations give partial solutions of conjectures
proposed by Imatomi, Tanaka, Wakabayashi and the first
author.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Ong:2013:GWS,
author = "Yao Lin Ong and Minking Eie and Wen-Chin Liaw",
title = "On Generalizations of Weighted Sum Formulas of
Multiple Zeta Values",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1185--1198",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211350019X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211350019X",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Aribam:2013:ISG,
author = "Chandrakant S. Aribam",
title = "On $ \mu $-invariants of {Selmer} groups of some {CM}
elliptic curves",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1199--1214",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500206",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500206",
abstract = "We show that the Selmer groups defined over the
cyclotomic {\mathbb{Z}}$_3$-extension of the field of
3-torsion points of the CM elliptic curves 256a1,
256a2, 256d1, 256d2, 121b1, 121b2 have \mu -invariant
equal to zero, verifying a conjecture in
non-commutative Iwasawa theory.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{McNew:2013:RWL,
author = "Nathan McNew",
title = "Radically Weakening the {Lehmer} and {Carmichael}
Conditions",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1215--1224",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500218",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500218",
abstract = "Lehmer's totient problem asks if there exist composite
integers n satisfying the condition \phi (n)|(n - 1)
(where \phi is the Euler-phi function), while
Carmichael numbers satisfy the weaker condition \lambda
(n)|(n - 1) (where \lambda is the Carmichael universal
exponent function). We weaken the condition further,
looking at those composite n where each prime divisor
of \phi (n) also divides n - 1. (So rad(\phi (n))|(n -
1).) While these numbers appear to be far more numerous
than the Carmichael numbers, we show that their
distribution has the same rough upper bound as that of
the Carmichael numbers, a bound which is heuristically
tight.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gross:2013:F,
author = "Samuel S. Gross and Andrew F. Vincent",
title = "On the factorization of $ f(n) $ for $ f(x) $ in {$
\mathbb {Z}[x] $}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1225--1236",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S179304211350022X",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S179304211350022X",
abstract = "Let S be a finite set of rational primes. For a
non-zero integer n, define, where |n|$_p$ is the usual
$p$-adic norm of n. In 1984, Stewart applied Baker's
theorem to prove non-trivial, computationally effective
upper bounds for [n(n+1)\cdots (n+k)]$_S$ for any
integer k > 0. Effective upper bounds have also been
given by Bennett, Filaseta, and Trifonov for [n(n +
1)]$_S$ and [n$^2$ + 7]$_S$, where S = {2, 3} and S =
{2}, respectively. We extend Stewart's theorem to prove
effective upper bounds for [f(n)]$_S$ for an arbitrary
f(x) in {\mathbb{Z}}[x] having at least two distinct
roots.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Shen:2013:LDP,
author = "Luming Shen and Jian Xu and Huiping Jing",
title = "On the Largest Degree of the Partial Quotients in
Continued Fraction Expansions Over the Field of Formal
{Laurent} Series",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1237--1247",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500231",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500231",
abstract = "For x \in I, let [A$_1$ (x), A$_2$ (x), \ldots ] be
the continued fraction expansions over the field of
Laurent series, write L$_n$ (x) \coloneq max{deg A$_1$
(x), deg A$_2$ (x), \ldots, deg A$_n$ (x)}, which is
called the largest degree of partial quotients. In this
paper, we give an iterated logarithm type theorem for
L$_n$ (x), and by which, we get that for P-almost all x
\in I,. Also the Hausdorff dimensions of the related
exceptional sets are determined.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bautista-Ancona:2013:GFC,
author = "V{\'i}ctor Bautista-Ancona and Martha
Rzedowski-Calder{\'o}n and Gabriel Villa-Salvador",
title = "Genus fields of cyclic $l$-extensions of rational
function fields",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1249--1262",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500243",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500243",
abstract = "We give a construction of genus fields for Kummer
cyclic l-extensions of rational congruence function
fields, l a prime number. First we find this genus
field for a field contained in a cyclotomic function
field using Leopoldt's construction by means of
Dirichlet characters and the Hilbert class field
defined by Rosen. The general case follows from this.
This generalizes the result obtained by Peng for a
cyclic extension of degree l.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Hu:2013:PRP,
author = "Jerry Hu",
title = "The probability that random positive integers are
$k$-wise relatively prime",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1263--1271",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500255",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500255",
abstract = "The positive integers a$_1$, a$_2$, \ldots, a$_s$ are
k-wise relatively prime if any k of them are relatively
prime. For a (k-1)-tuple of positive integers u =
(u$_1$, \ldots, u$_{k - 1}$), let denote the number of
s-tuples of positive integers (a$_1$, a$_2$, \ldots,
a$_s$) with 1 \leq a$_1$, a$_2$, \ldots, a$_s$ \leq n
such that a$_1$, a$_2$, \ldots, a$_s$ are k-wise
relatively prime and are i-wise relatively prime to
u$_i$ for i = 1, 2, \ldots, k-1 when s \geq k \geq 2,
and a$_1$, a$_2$, \ldots, a$_s$ are i-wise relatively
prime to u$_i$ for i = 1, 2, \ldots, s when k > s \geq
1. Asymptotic estimates are obtained for these
functions. As a corollary, exact formula is also
obtained for the probability that s positive integers
are k-wise relatively prime.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Rogers:2013:SSC,
author = "Mathew D. Rogers and Armin Straub",
title = "A solution of {Sun}'s \$520 challenge concerning $
\frac {520}{\pi } $",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1273--1288",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500267",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500267",
abstract = "We prove a Ramanujan-type formula for 520/\pi
conjectured by Zhi-Wei Sun. Our proof begins with a
hypergeometric representation of the relevant double
series, which relies on a recent generating function
for Legendre polynomials by Wan and Zudilin. After
showing that appropriate modular parameters can be
introduced, we then apply standard techniques, going
back to Ramanujan, for establishing series for 1/\pi.
Finally, we demonstrate that our approach can be used
to also establish all further conjectures by Sun on
series for 1/\pi of the same form.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Barman:2013:ALI,
author = "Rupam Barman",
title = "Another look at {Iwasawa} $ \lambda $-invariants of
$p$-adic measures on {$ \mathbb {Z}_p^n$} and {$ \Gamma
$}-transforms",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1289--1299",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500279",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500279",
abstract = "In [Iwasawa \lambda -invariants of $p$-adic measures
on and their \Gamma -transforms, {\em J. Number
Theory\/} 132(10) (2012) 2258--2266; Iwasawa \lambda
-invariants and \Gamma -transforms of $p$-adic measure
on, {\em Int. J. Number Theory\/} 6(8) (2010)
1819--1829], the author and Saikia defined Iwasawa
\lambda -Invariants for multi-variable power series and
proved a relation between the Iwasawa \lambda
-invariant of a $p$-adic measure on and its \Gamma
transform. In this paper, we give two new definitions
of \lambda invariants for multi-variable power series
which generalize the \lambda -invariant of single
variable power series and prove that the new \lambda
-invariants also satisfy the same relation. We also
give algebraic interpretations of the new \lambda
-invariants and discuss an application of our main
results.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Toth:2013:TGB,
author = "L{\'a}szl{\'o} T{\'o}th",
title = "Two Generalizations of the {Busche--Ramanujan}
Identities",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1301--1311",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500280",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500280",
abstract = "We derive two new generalizations of the
Busche--Ramanujan identities involving the multiple
Dirichlet convolution of arithmetic functions of
several variables. The proofs use formal multiple
Dirichlet series and properties of symmetric
polynomials of several variables.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Berndt:2013:EPR,
author = "Bruce C. Berndt and Byungchan Kim and Kenneth S.
Williams",
title = "{Euler} Products in {Ramanujan}'s {{\booktitle{Lost
Notebook}}}",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1313--1349",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500292",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500292",
abstract = "In his famous paper, ``On certain arithmetical
functions'', Ramanujan offers for the first time the
Euler product of the Dirichlet series in which the
coefficients are given by Ramanujan's tau-function. In
his lost notebook, Ramanujan records further Euler
products for $L$-series attached to modular forms, and,
typically, does not record proofs for these claims. In
this semi-expository article, for the Euler products
appearing in his lost notebook, we provide or sketch
proofs using elementary methods, binary quadratic
forms, and modular forms.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Bravo:2013:LPF,
author = "Jhon J. Bravo and Florian Luca",
title = "On the largest prime factor of the $k$-{Fibonacci}
numbers",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "5",
pages = "1351--1366",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500309",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:24 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500309",
abstract = "Let P(m) denote the largest prime factor of an integer
m \geq 2, and put P(0) = P(1) = 1. For an integer k
\geq 2, let be the k-generalized Fibonacci sequence
which starts with 0, \ldots, 0, 1 (k terms) and each
term afterwards is the sum of the k preceding terms.
Here, we show that if n \geq k+2, then. Furthermore, we
determine all the k-Fibonacci numbers whose largest
prime factor is less than or equal to 7.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Gillespie:2013:FAF,
author = "Tim Gillespie",
title = "Factorization of Automorphic {$L$}-Functions and Their
Zero Statistics",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "6",
pages = "1367--1378",
month = sep,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1142/S1793042113500310",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500310",
abstract = "In this paper we define a Rankin--Selberg
{$L$}-function attached to two Galois invariant
automorphic cuspidal representations of GL$_m$ ({$
\mathbb {A} $}$_$E) and GL$_{m \prime }$ ({$ \mathbb
{A} $}$_F$) over cyclic Galois extensions E and F of
prime degree. This differs from the classical case in
that the two extension fields E and F could be
completely unrelated to one another, and we exploit the
existence of the automorphic induction functor over
cyclic extensions (see [J. Arthur and L. Clozel, {\em
Simple Algebras, Base Change, and the Advanced Theory
of the Trace Formula\/}, Annals of Mathematics Studies,
No. 120 (Princeton University Press, Princeton, NJ,
1989)]) to define the {$L$}-function. Using a result
proved by C. S. Rajan, we prove a prime number theorem
for this {$L$}-function, and proceed to calculate the
n-level correlation function of high nontrivial zeros
of a product L(s, \pi$_1$)L(s, \pi$_2$)\ldots L(s,
\pi$_k$ ) where \pi$_i$ is a Galois invariant cuspidal
representation of GL$_{n i}$ ({$ \mathbb {A} $}$_{F i}$
) with F$_i$ a cyclic Galois extension of prime degree
\ell$_i$ for i = 1,\ldots, k, thus generalizing the
results of Liu and Ye [Functoriality of automorphic
{$L$}-functions through their zeros, {\em Sci. China
Ser. A\/} 51(1) (2008) 1--16].",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://www.worldscientific.com/worldscinet/ijnt",
}
@Article{Alvarado:2013:APC,
author = "Alejandra Alvarado and Edray Herber Goins",
title = "Arithmetic Progressions on Conic Sections",
journal = j-INT-J-NUMBER-THEORY,
volume = "9",
number = "6",
pages = "1379--1393",
month = sep,
year = "2013",
DOI = "https://doi.org/10.1142/S1793042113500322",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
bibdate = "Tue Jul 21 10:23:25 MDT 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "https://www.worldscientific.com/doi/10.1142/S1793042113500322",
abstract = "The set {1, 25, 49} is a 3-term collection of integers
which forms an arithmetic progression of perfect
squares. We view the set {(1, 1), (5, 25), (7, 49)} as
a 3-term collection of rational points on the parabola