@Preamble{
"\ifx \undefined \binom \def \binom #1#2{{#1\choose#2}} \fi" #
"\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)} \fi" #
"\ifx \undefined \Co \def \Co {\mathrm{Co}} \fi" #
"\ifx \undefined \Dbar \def \Dbar {\leavevmode\raise0.2ex\hbox{--}\kern-0.5emD} \fi" #
"\ifx \undefined \Gal \def \Gal {\mathrm{Gal}} \fi" #
"\ifx \undefined \gcd \def \gcd {\mathrm{gcd}} \fi" #
"\ifx \undefined \k \let \k = \c \fi" #
"\ifx \undefined \lcm \def \lcm {\mathrm{lcm}} \fi" #
"\ifx \undefined \li \def \li {\mathrm{li}} \fi" #
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" #
"\ifx \undefined \mathbf \def \mathbf #1{{\bf #1}} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" #
"\ifx \undefined \mathfrak \let \mathfrak = \mathbf \fi" #
"\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi" #
"\ifx \undefined \mathsf \def \mathsf #1{{\sf #1}} \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}} \fi" #
"\ifx \undefined \Res \def \Res {\mathrm{Res}} \fi" #
"\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi"
}
@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/|"}
@String{j-INT-J-NUMBER-THEORY = "International Journal of Number Theory (IJNT)"}
@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",
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",
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",