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%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.01",
%%%     date            = "08 August 2020",
%%%     time            = "10:28:01 MDT",
%%%     filename        = "ijnt.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "59233 51662 273405 2538126",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "BibTeX; bibliography; International Journal
%%%                        of Number Theory (IJNT)",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of the International
%%%                        Journal of Number Theory (IJFCS) (CODEN
%%%                        none, ISSN 1793-0421 (print), 1793-7310
%%%                        (electronic)), published by World
%%%                        Scientific.
%%%
%%%                        Publication began with volume 1, number 1, in
%%%                        March 2005, and the number of issues per
%%%                        volume has increased from 4 (2005--2007) to 6
%%%                        (2008) to 8 (2009--2015) to 10 (2016--).
%%%
%%%                        The journal has World-Wide Web site at
%%%
%%%                            http://ejournals.wspc.com.sg/ijnt
%%%                            https://www.worldscientific.com/worldscinet/ijnt
%%%
%%%                        At version 1.01, the COMPLETE year coverage
%%%                        looked like this:
%%%
%%%                             2005 (  37)    2011 ( 124)    2017 ( 154)
%%%                             2006 (  39)    2012 ( 119)    2018 ( 168)
%%%                             2007 (  39)    2013 ( 122)    2019 ( 132)
%%%                             2008 (  72)    2014 ( 125)    2020 (  87)
%%%                             2009 (  89)    2015 ( 143)
%%%                             2010 ( 111)    2016 ( 143)
%%%
%%%                             Article:       1704
%%%
%%%                             Total entries: 1704
%%%
%%%                        Data for the bibliography has been collected
%%%                        primarily from the journal Web site, with
%%%                        additional data entries from BibNet Project
%%%                        and TeX User Group bibliography archives.
%%%
%%%                        Numerous errors in the sources noted above
%%%                        have been corrected.   Spelling has been
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%%%
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%%%
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%%%                        updowncase and downcase style; most author
%%%                        and title data at the publisher Web site are
%%%                        uppercase, often losing critical information.
%%%
%%%                        About one percent of the articles in this
%%%                        journal are in French; English translations
%%%                        of titles are provided for them.
%%%
%%%                        BibTeX citation tags are uniformly chosen
%%%                        as name:year:abbrev, where name is the
%%%                        family name of the first author or editor,
%%%                        year is a 4-digit number, and abbrev is a
%%%                        3-letter condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        In this bibliography, entries are sorted in
%%%                        publication order, using ``bibsort -byvolume''.
%%%
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%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-INT-J-NUMBER-THEORY  = "International Journal of Number Theory (IJNT)"}

%%% ====================================================================
%%% Bibliography entries:
@Article{Bourgain:2005:MSP,
  author =       "J. Bourgain",
  title =        "More on the Sum--Product Phenomenon in Prime Fields
                 and Its Applications",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "1--32",
  month =        mar,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042105000108",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000108",
  abstract =     "In this paper we establish new estimates on
                 sum-product sets and certain exponential sums in finite
                 fields of prime order. Our first result is an extension
                 of the sum-product theorem from [8] when sets of
                 different sizes are involved. It is shown that if and
                 p$^{\varepsilon }$ < |B|, |C| < |A| < p$^{1 -
                 \varepsilon }$, then |A + B| + |A \cdotp C| >
                 p$^{\delta (\varepsilon)}$ |A|. Next we exploit the
                 Szemer{\'e}di--Trotter theorem in finite fields (also
                 obtained in [8]) to derive several new facts on
                 expanders and extractors. It is shown for instance that
                 the function f(x,y) = x(x+y) from to satisfies |F(A,B)|
                 > p$^{\beta }$ for some \beta = \beta (\alpha) > \alpha
                 whenever and $ |A| \sim |B| \sim p^\alpha $, $ 0 <
                 \alpha < 1$. The exponential sum $ \sum_{x \in A, y \in
                 B}$ \varepsilon$_p$ (axy+bx$^2$ y$^2$), ab \neq 0 (mod
                 p), may be estimated nontrivially for arbitrary sets
                 satisfying |A|, |B| > p$^{\rho }$ where \rho < 1/2 is
                 some constant. From this, one obtains an explicit
                 2-source extractor (with exponential uniform
                 distribution) if both sources have entropy ratio at
                 last \rho. No such examples when \rho < 1/2 seemed
                 known. These questions were largely motivated by recent
                 works on pseudo-randomness such as [2] and [3]. Finally
                 it is shown that if p$^{\varepsilon }$ < |A| < p$^{1 -
                 \varepsilon }$, then always |A + A|+|A$^{-1}$ +
                 A$^{-1}$ | > p$^{\delta (\varepsilon)}$ |A|. This is
                 the finite fields version of a problem considered in
                 [11]. If A is an interval, there is a relation to
                 estimates on incomplete Kloosterman sums. In the
                 Appendix, we obtain an apparently new bound on bilinear
                 Kloosterman sums over relatively short intervals
                 (without the restrictions of Karatsuba's result [14])
                 which is of relevance to problems involving the divisor
                 function (see [1]) and the distribution (mod p) of
                 certain rational functions on the primes (cf. [12]).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2005:EFQ,
  author =       "Heng Huat Chan and Zhi-Guo Liu and Say Tiong Ng",
  title =        "Elliptic Functions and the Quintuple, {Hirschhorn} and
                 {Winquist} Product Identities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "33--43",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000017",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000017",
  abstract =     "In this article, we derive the quintuple, Hirschhorn
                 and Winquist product identities using the theory of
                 elliptic functions. Our method can be used to establish
                 generalizations of these identities due to the second
                 author.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alkan:2005:NRT,
  author =       "Emre Alkan and Alexandru Zaharescu",
  title =        "Nonvanishing of the {Ramanujan} {Tau} Function in
                 Short Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "45--51",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000029",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000029",
  abstract =     "We provide new estimates for the gap function of the
                 Delta function and for the number of nonzero values of
                 the Ramanujan tau function in short intervals.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chen:2005:SEG,
  author =       "Sin-Da Chen and Sen-Shan Huang",
  title =        "On the series expansion of the {G{\"o}llnitz--Gordon}
                 continued fraction",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "53--63",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000030",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000030",
  abstract =     "We give combinatorial interpretations of the
                 coefficients in the series expansions of the
                 G{\"o}llnitz--Gordon continued fraction and its
                 reciprocal. These combinatorial results enable us to
                 determine the signs of the coefficients. At the end, we
                 also derive some interesting identities involving the
                 coefficients.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ivic:2005:MTS,
  author =       "Aleksandar Ivi{\'c}",
  title =        "The {Mellin} Transform of the Square of {Riemann}'s
                 Zeta-Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "65--73",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000042",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000042",
  abstract =     "Let. A result concerning analytic continuation of $
                 Z_1 $ (s) to {\mathbb{C}} is proved, and also a result
                 relating the order of to the order of.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ono:2005:APC,
  author =       "Ken Ono and Yuichiro Taguchi",
  title =        "$2$-Adic Properties of Certain Modular Forms and Their
                 Applications to Arithmetic Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "75--101",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000066",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000066",
  abstract =     "It is a classical observation of Serre that the Hecke
                 algebra acts locally nilpotently on the graded ring of
                 modular forms modulo 2 for the full modular group. Here
                 we consider the problem of classifying spaces of
                 modular forms for which this phenomenon continues to
                 hold. We give a number of consequences of this
                 investigation as they relate to quadratic forms,
                 partition functions, and central values of twisted
                 modular {$L$}-functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jenkins:2005:APT,
  author =       "Paul Jenkins",
  title =        "$p$-adic properties for traces of singular moduli",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "103--107",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S179304210500011X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210500011X",
  abstract =     "We examine the $p$-adic properties of Zagier's traces
                 $ \Tr (d)$ of the singular moduli of discriminant $ -
                 d$. In a recent preprint, Edixhoven proved that if $p$
                 is prime and $ \frac {-d}{p} = 1$, then $ \Tr (p^{2n}
                 d) \equiv 0 (\bmod p^n)$. We compute an exact formula
                 for $ \Tr (p^{2n}d)$ which immediately gives
                 Edixhoven's result as a corollary.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kedlaya:2005:LMA,
  author =       "Kiran S. Kedlaya",
  title =        "Local monodromy of $p$-adic differential equations: an
                 overview",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "109--154",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S179304210500008X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210500008X",
  abstract =     "This primarily expository article collects together
                 some facts from the literature about the monodromy of
                 differential equations on a $p$-adic (rigid analytic)
                 annulus, though often with simpler proofs. These
                 include Matsuda's classification of quasi-unipotent
                 \nabla -modules, the Christol--Mebkhout construction of
                 the ramification filtration, and the Christol--Dwork
                 Frobenius antecedent theorem. We also briefly discuss
                 the $p$-adic local monodromy theorem without proof.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Brueggeman:2005:NCN,
  author =       "Sharon Brueggeman",
  title =        "The Nonexistence of Certain Nonsolvable {Galois}
                 Extensions of Number Fields of Small Degree",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "1",
  pages =        "155--160",
  month =        mar,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000121",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000121",
  abstract =     "Serre's conjecture predicts the nonexistence of
                 certain nonsolvable Galois extensions of {$ \mathbb {Q}
                 $} which are unramified outside one small prime. These
                 nonexistence theorems have been proven by the
                 techniques of discriminant bounding. In this paper, we
                 will apply these techniques to nonsolvable extensions
                 of small degree number fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Choi:2005:STS,
  author =       "S. K. K. Choi and A. V. Kumchev and R. Osburn",
  title =        "On Sums of Three Squares",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "161--173",
  month =        jun,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042105000054",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000054",
  abstract =     "Let r$_3$ (n) be the number of representations of a
                 positive integer n as a sum of three squares of
                 integers. We give two alternative proofs of a
                 conjecture of Wagon concerning the asymptotic value of
                 the mean square of r$_3$ (n).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Adiga:2005:GRB,
  author =       "Chandrashekar Adiga and Shaun Cooper and Jung Hun
                 Han",
  title =        "A General Relation Between Sums of Squares and Sums of
                 Triangular Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "175--182",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000078",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000078",
  abstract =     "Let r$_k$ (n) and t$_k$ (n) denote the number of
                 representations of n as a sum of k squares, and as a
                 sum of k triangular numbers, respectively. We give a
                 generalization of the result r$_k$ (8n + k) = c$_k$
                 t$_k$ (n), which holds for 1 \leq k \leq 7, where c$_k$
                 is a constant that depends only on k. Two proofs are
                 provided. One involves generating functions and the
                 other is combinatorial.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Maier:2005:CGE,
  author =       "H. Maier and A. Sankaranarayanan",
  title =        "On a Certain General Exponential Sum",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "183--192",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000224",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000224",
  abstract =     "In this paper we study the general exponential sum
                 related to multiplicative functions $ f(n) $ with $
                 |f(n)| \leq 1 $, namely we study the sum $ F(x, \alpha)
                 = \sum_{n \leq x} f(n) e(n \alpha) $ and obtain a
                 non-trivial upper bound when $ \alpha $ is a certain
                 type of rational number.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Williams:2005:CS,
  author =       "Kenneth S. Williams",
  title =        "The Convolution Sum $ \sum_{m < n / 9} \sigma (m)
                 \sigma (n - 9 m) $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "193--205",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000091",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000091",
  abstract =     "The evaluation of the sum $ \sum_{m < n / 9} \sigma
                 (m) \sigma (n - 9 m) $ is carried out for all positive
                 integers $n$. This evaluation is used to detemine the
                 number of solutions to $ n = x_1^2 + x_1 x_2 + x_2^2 +
                 x_3^2 + x_3 x_4 + x_4^2 + 3 (x_5^2 + x_5 x_6 + x_6^2 +
                 x_7^2 + x_7 x_8 + x_8^2)$ in integers $ x_1$, $ x_2$, $
                 x_3$, $ x_4$, $ x_5$, $ x_6$, $ x_7$, $ x_8$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2005:HMP,
  author =       "Tsz Ho Chan",
  title =        "Higher Moments of Primes in Short Intervals {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "207--214",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000169",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000169",
  abstract =     "Given good knowledge on the even moments, we derive
                 asymptotic formulas for \lambda th moments of primes in
                 short intervals and prove ``equivalence'' result on odd
                 moments. We also provide numerical evidence in support
                 of these results.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lovejoy:2005:TSC,
  author =       "Jeremy Lovejoy",
  title =        "A Theorem on Seven-Colored Overpartitions and Its
                 Applications",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "215--224",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000157",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000157",
  abstract =     "A $q$-series identity in four parameters is
                 established and interpreted as a statement about
                 7-colored overpartitions. As corollaries some
                 overpartition theorems of the Rogers--Ramanujan type
                 and some weighted overpartition theorems are exhibited.
                 Among these are overpartition analogues of classical
                 partition theorems of Schur and G{\"o}llnitz.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Eie:2005:EGE,
  author =       "Minking Eie and Wen-Chin Liaw and Fu-Yao Yang",
  title =        "On Evaluation of Generalized {Euler} Sums of Even
                 Weight",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "225--242",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000182",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000182",
  abstract =     "The classical Euler sum $ S_{p, q} = \sum_{k =
                 1}^\infty \frac {1}{k^q} \sum_{j = 1}^k \frac {1}{j^p}
                 $ cannot be evaluated when the weight $ p + q $ is even
                 unless $ p = 1 $ or $ p = q $ or $ (p, q) = (2, 4) $ or
                 $ (p, q) = (4, 2) $ [7]. However it is a different
                 story if instead we consider the alternating sums $
                 G_{p, q}^{-, -} = \sum_{k = 0}^\infty \frac {( -
                 1)^k}{(2 k + 1)^q} \sum_{j = 1}^k \frac {( - 1)^{j +
                 1}}{j^p} $ and $ G_{p, q}^{+, -} = \sum_{k = 0}^\infty
                 \frac {( - 1)^k}{(2 k + 1)^q} \sum_{j = 1}^k \frac
                 {1}{j^p} $. They can be evaluated for even weight $ p +
                 q $. In this paper, we shall evaluate a family of
                 generalized Euler sums containing $ G_{p, q}^{-, -} $
                 when the weight $ p + q $ is even via integral
                 transforms of Bernoulli identities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Delaunay:2005:MOT,
  author =       "Christophe Delaunay",
  title =        "Moments of the Orders of {Tate--Shafarevich} Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "243--264",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000133",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000133",
  abstract =     "We give some conjectures for the moments of the orders
                 of the Tate--Shafarevich groups of elliptic curves
                 belonging to a family of quadratic twists. These
                 conjectures follow from the predictions on
                 {$L$}-functions given by the random matrix theory
                 [12,5] and from the Birch and Swinnerton--Dyer
                 conjecture. Furthermore, including the Cohen--Lenstra
                 type heuristics for Tate--Shafarevich groups, we obtain
                 some conjectural estimates for the regulator of rank 1
                 elliptic curves in a family of quadratic twists.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baier:2005:LSI,
  author =       "Stephan Baier and Liangyi Zhao",
  title =        "Large Sieve Inequality with Characters for Powerful
                 Moduli",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "265--279",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000170",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000170",
  abstract =     "In this paper we aim to generalize the results in [1,
                 2, 19] and develop a general formula for large sieve
                 with characters to powerful moduli that will be an
                 improvement to the result in [19].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Petsche:2005:QVB,
  author =       "Clayton Petsche",
  title =        "A Quantitative Version of {Bilu}'s Equidistribution
                 Theorem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "281--291",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000145",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000145",
  abstract =     "We use Fourier-analytic methods to give a new proof of
                 Bilu's theorem on the complex equidistribution of small
                 points on the one-dimensional algebraic torus. Our
                 approach yields a quantitative bound on the error term
                 in terms of the height and the degree.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baoulina:2005:PC,
  author =       "Ioulia Baoulina",
  title =        "On a Problem of {Carlitz}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "2",
  pages =        "293--307",
  month =        jun,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000194",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:12 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000194",
  abstract =     "Let $ N_q $ be the number of solutions to the equation
                 $ (x_1 + \cdots + x_n)^2 = a x_1 \ldots {} x_n $ over
                 the finite field $ \mathbb {F}_q = \mathbb {F}_p $.
                 Carlitz found formulas for $ N_q $ when $ n = 3 $ or
                 $4$. In an earlier paper, we found formulas for $ N_q$
                 when $ d = \gcd (n 2, q - 1) = 1$ or $2$ or $3$ or $4$;
                 and when there exists an $l$ such that $ p^l - 1 (\bmod
                 d)$. In another paper the cases $ d = 7$ or $ 14$, $ p
                 2$ or $4$ $ (\bmod 7)$ were considered. In this paper,
                 we find formulas for $ N_q$ when $ d = 8$. We also
                 simplify formulas for $ N_q$ when $ d = 4$, $ p 1$ $
                 (\bmod 4)$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bugeaud:2005:PPL,
  author =       "Yann Bugeaud and Florian Luca and Maurice Mignotte and
                 Samir Siksek",
  title =        "On Perfect Powers in {Lucas} Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "309--332",
  month =        sep,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042105000236",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000236",
  abstract =     "Let (u$_n$)$_{n \geq 0}$ be the binary recurrence
                 sequence of integers given by u$_0$ = 0, u$_1$ = 1 and
                 u$_{n + 2}$ = 2(u$_{n + 1}$ + u$_n$). We show that the
                 only positive perfect powers in this sequence are u$_1$
                 = 1 and u$_4$ = 16. We further discuss the problem of
                 determining perfect powers in Lucas sequences in
                 general.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Beck:2005:DAG,
  author =       "Matthias Beck and Bruce C. Berndt and O-Yeat Chan and
                 Alexandru Zaharescu",
  title =        "Determinations of Analogues of {Gauss} Sums and Other
                 Trigonometric Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "333--356",
  month =        sep,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000200",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000200",
  abstract =     "Explicit determinations of several classes of
                 trigonometric sums are given. These sums can be viewed
                 as analogues or generalizations of Gauss sums. In a
                 previous paper, two of the present authors considered
                 primarily sine sums associated with primitive odd
                 characters. In this paper, we establish two general
                 theorems involving both sines and cosines, with more
                 attention given to cosine sums in the several examples
                 that we provide.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Roy:2005:SAC,
  author =       "Damien Roy",
  title =        "Simultaneous Approximation by Conjugate Algebraic
                 Numbers in Fields of Transcendence Degree One",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "357--382",
  month =        sep,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000212",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000212",
  abstract =     "We present a general result of simultaneous
                 approximation to several transcendental real, complex
                 or $p$-adic numbers \xi$_1$, \ldots, \xi$_t$ by
                 conjugate algebraic numbers of bounded degree over {$
                 \mathbb {Q}$}, provided that the given transcendental
                 numbers \xi$_1$, \ldots, \xi$_t$ generate over {$
                 \mathbb {Q}$} a field of transcendence degree one. We
                 provide sharper estimates for example when \xi$_1$,
                 \ldots, \xi$_t$ form an arithmetic progression with
                 non-zero algebraic difference, or a geometric
                 progression with non-zero algebraic ratio different
                 from a root of unity. In this case, we also obtain by
                 duality a version of Gel'fond's transcendence criterion
                 expressed in terms of polynomials of bounded degree
                 taking small values at \xi$_1$, \ldots, \xi$_t$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alkan:2005:AFS,
  author =       "Emre Alkan and Alexandru Zaharescu and Mohammad Zaki",
  title =        "Arithmetical Functions in Several Variables",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "383--399",
  month =        sep,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S179304210500025X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210500025X",
  abstract =     "In this paper we investigate the ring A$_r$ (R) of
                 arithmetical functions in r variables over an integral
                 domain R. We study a class of absolute values, and a
                 class of derivations on A$_r$ (R). We show that a
                 certain extension of A$_r$ (R) is a discrete valuation
                 ring. We also investigate the metric structure of the
                 ring A$_r$ (R).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Suzuki:2005:RBZ,
  author =       "Masatoshi Suzuki",
  title =        "A Relation Between the Zeros of Two Different
                 {$L$}-Functions Which Have an {Euler} Product and
                 Functional Equation",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "401--429",
  month =        sep,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000248",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000248",
  abstract =     "As automorphic {$L$}-functions or Artin
                 {$L$}-functions, several classes of {$L$}-functions
                 have Euler products and functional equations. In this
                 paper we study the zeros of {$L$}-functions which have
                 Euler products and functional equations. We show that
                 there exists a relation between the zeros of the
                 Riemann zeta-function and the zeros of such
                 {$L$}-functions. As a special case of our results, we
                 find relations between the zeros of the Riemann
                 zeta-function and the zeros of automorphic
                 {$L$}-functions attached to elliptic modular forms or
                 the zeros of Rankin--Selberg {$L$}-functions attached
                 to two elliptic modular forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Niederreiter:2005:ESD,
  author =       "Harald Niederreiter and Arne Winterhof",
  title =        "Exponential sums and the distribution of inversive
                 congruential pseudorandom numbers with power of two
                 modulus",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "431--438",
  month =        sep,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042105000261",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11K38 (11K45 11L07)",
  MRnumber =     "2175100 (2006f:11092)",
  MRreviewer =   "Igor E. Shparlinski",
  bibdate =      "Thu Dec 22 06:50:44 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000261",
  abstract =     "Niederreiter and Shparlinski obtained a nontrivial
                 discrepancy bound for sequences of inversive
                 congruential pseudorandom numbers with odd prime-power
                 modulus. Because of technical difficulties they had to
                 leave open the case of greatest practical interest,
                 namely where the modulus is a power of 2. In the
                 present paper we successfully treat this case by using
                 recent advances in the theory of exponential sums.",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Number Theory",
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Eie:2005:EDE,
  author =       "Minking Eie and Yao Lin Ong and Fu Yao Yang",
  title =        "Evaluating Double {Euler} Sums Over Rationally
                 Deformed Simplices",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "3",
  pages =        "439--458",
  month =        sep,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000273",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000273",
  abstract =     "As a natural generalization of the classical Euler sum
                 defined by $ S_{p, q} = \sum_{k = 1}^\infty \frac
                 {1}{k^q} \sum_{j = 1}^k \frac {1}{j^p} $, we change the
                 upper limit of the inner summation into $ k r $, a
                 fixed rational multiple of $k$, and obtain countable
                 families of new sums which we call the extended Euler
                 sums. We shall develop a systematic new method to
                 evaluate these extended Euler sums as well as
                 corresponding alternating sums in terms of values at
                 non-negative integers of cosine and sine parts of the
                 periodic zeta function when the weight $ p + q$ is
                 odd.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Friedlander:2005:IS,
  author =       "J. B. Friedlander and H. Iwaniec",
  title =        "The Illusory Sieve",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "459--494",
  month =        dec,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042105000303",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000303",
  abstract =     "We study some of the extremely strong statements that
                 can be made about the distribution of primes assuming
                 the (unlikely) existence of exceptional Dirichlet
                 characters. We treat this in general and then apply the
                 results to the particular cases of primes of the form $
                 a^2 + b^6 $ and of elliptic curves having prime
                 discriminant.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Edixhoven:2005:AGT,
  author =       "Bas Edixhoven",
  title =        "On the $p$-adic geometry of traces of singular
                 moduli",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "495--497",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000327",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000327",
  abstract =     "The aim of this article is to show that $p$-adic
                 geometry of modular curves is useful in the study of
                 $p$-adic properties of {\em traces\/} of singular
                 moduli. In order to do so, we partly answer a question
                 by Ono [7, Problem 7.30]. As our goal is just to
                 illustrate how $p$-adic geometry can be used in this
                 context, we focus on a relatively simple case, in the
                 hope that others will try to obtain the strongest and
                 most general results. For example, for p = 2, a result
                 stronger than Theorem 2 is proved in [2], and a result
                 on some modular curves of genus zero can be found in
                 [8]. It should be easy to apply our method, because of
                 its local nature, to modular curves of arbitrary level,
                 as well as to Shimura curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Litsyn:2005:IFS,
  author =       "Simon Litsyn and Vladimir Shevelev",
  title =        "Irrational factors satisfying the little {Fermat}
                 theorem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "499--512",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000339",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000339",
  abstract =     "We study possible generalizations of the little Fermat
                 theorem when the base of the exponentiation is allowed
                 to be a non-integer. Such bases we call Fermat factors.
                 We attempt classification of Fermat factors, and
                 suggest several constructions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dummigan:2005:RTO,
  author =       "Neil Dummigan",
  title =        "Rational Torsion on Optimal Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "513--531",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000340",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000340",
  abstract =     "Vatsal has proved recently a result which has
                 consequences for the existence of rational points of
                 odd prime order \ell on optimal elliptic curves over {$
                 \mathbb {Q} $}. When the conductor N is squarefree,
                 \ell \nmid N and the local root number w$_p$ = -1 for
                 at least one prime p | N, we offer a somewhat different
                 proof, starting from an explicit cuspidal divisor on
                 X$_0$ (N). We also prove some results linking the
                 vanishing of L(E,1) with the divisibility by \ell of
                 the modular parametrization degree, fitting well with
                 the Bloch--Kato conjecture for L(Sym$^2$ E,2), and with
                 an earlier construction of elements in
                 Shafarevich--Tate groups. Finally (following Faltings
                 and Jordan) we prove an analogue of the result on \ell
                 -torsion for cuspidal Hecke eigenforms of level one
                 (and higher weight), thereby strengthening some
                 existing evidence for another case of the Bloch--Kato
                 conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Long:2005:SPM,
  author =       "Ling Long and Yifan Yang",
  title =        "A Short Proof of {Milne}'s Formulas for Sums of
                 Integer Squares",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "533--551",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000364",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000364",
  abstract =     "We give a short proof of Milne's formulas for sums of
                 4n$^2$ and 4n$^2$ + 4n integer squares using the theory
                 of modular forms. Other identities of Milne are also
                 discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mollin:2005:EAL,
  author =       "R. A. Mollin",
  title =        "On an Elementary Approach to the {Lebesgue--Nagell}
                 Equation",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "553--561",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000352",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000352",
  abstract =     "We discuss the feasibility of an elementary solution
                 to the Diophantine equation of the form x$^2$ + D =
                 y$^n$, where D > 1, n \geq 3 and x > 0, called the
                 Lebesgue--Nagell equation, which has recently been
                 solved for 1 \leq D \leq 100 in [1].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Knopfmacher:2005:SFC,
  author =       "A. Knopfmacher and M. E. Mays",
  title =        "A Survey of Factorization Counting Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "563--581",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000315",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000315",
  abstract =     "The general field of additive number theory considers
                 questions concerning representations of a given
                 positive integer n as a {\em sum\/} of other integers.
                 In particular, {\em partitions\/} treat the sums as
                 unordered combinatorial objects, and {\em
                 compositions\/} treat the sums as ordered. Sometimes
                 the sums are restricted, so that, for example, the
                 summands are distinct, or relatively prime, or all
                 congruent to \pm 1 modulo 5. In this paper we review
                 work on analogous problems concerning representations
                 of n as a {\em product\/} of positive integers. We
                 survey techniques for enumerating product
                 representations both in the unrestricted case and in
                 the case when the factors are required to be distinct,
                 and both when the product representations are
                 considered as ordered objects and when they are
                 unordered. We offer some new identities and
                 observations for these and related counting functions
                 and derive some new recursive algorithms to generate
                 lists of factorizations with restrictions of various
                 types.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Luca:2005:PDL,
  author =       "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}",
  title =        "Prime Divisors of {Lucas} Sequences and a Conjecture
                 of {Ska{\l}ba}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "583--591",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000285",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000285",
  abstract =     "In this paper, we give some heuristics suggesting that
                 if (u$_n$)$_{n \geq 0}$ is the Lucas sequence given by
                 u$_n$ = (a$^n$- 1)/(a - 1), where a > 1 is an integer,
                 then \omega (u$_n$) \geq (1 + o(1))log n log log n
                 holds for almost all positive integers n.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zhang:2005:EET,
  author =       "Liang-Cheng Zhang",
  title =        "Explicit Evaluations of Two {Ramanujan--Selberg}
                 Continued Fractions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "593--601",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000297",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000297",
  abstract =     "This paper gives explicit evaluations for two
                 Ramanujan--Selberg continued fractions in terms of
                 class invariants and singular moduli.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2005:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 1)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "1",
  number =       "4",
  pages =        "603--605",
  month =        dec,
  year =         "2005",
  DOI =          "https://doi.org/10.1142/S1793042105000376",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:13 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042105000376",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kohnen:2006:TSA,
  author =       "Winfried Kohnen and Riccardo Salvati Manni",
  title =        "On the Theta Series Attached to {$ D_m^+ $}-Lattices",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "1--5",
  month =        mar,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042106000449",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000449",
  abstract =     "We show that the theta series attached to the -lattice
                 for any positive integer divisible by 8 can be
                 explicitly expressed as a finite rational linear
                 combination of products of two Eisenstein series.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cohen:2006:PRQ,
  author =       "Joseph Cohen",
  title =        "Primitive Roots in Quadratic Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "7--23",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000425",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000425",
  abstract =     "We consider an analogue of Artin's primitive root
                 conjecture for units in real quadratic fields. Given
                 such a nontrivial unit, for a rational prime p which is
                 inert in the field the maximal order of the unit modulo
                 p is p + 1. An extension of Artin's conjecture is that
                 there are infinitely many such inert primes for which
                 this order is maximal. This is known at present only
                 under the Generalized Riemann Hypothesis.
                 Unconditionally, we show that for any choice of 7 units
                 in different real quadratic fields satisfying a certain
                 simple restriction, there is at least one of the units
                 which satisfies the above version of Artin's
                 conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vulakh:2006:DA,
  author =       "L. Ya. Vulakh",
  title =        "{Diophantine} approximation in {$ Q(\sqrt {-5}) $} and
                 {$ Q(\sqrt {-5}) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "25--48",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000462",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000462",
  abstract =     "The complete description of the discrete part of the
                 Lagrange and Markov spectra of the imaginary quadratic
                 fields with discriminants -20 and -24 are given. Farey
                 polygons associated with the extended Bianchi groups
                 B$_d$, d = 5, 6, are used to reduce the problem of
                 finding the discrete part of the Markov spectrum for
                 the group B$_d$ to the corresponding problem for one of
                 its maximal Fuchsian subgroup. Hermitian points in the
                 Markov spectrum of B$_d$ are introduced for any d. Let
                 H$^3$ be the upper half-space model of the
                 three-dimensional hyperbolic space. If \nu is a
                 Hermitian point in the spectrum, then there is a set of
                 extremal geodesics in H$^3$ with diameter 1/\nu, which
                 depends on one continuous parameter. This phenomenon
                 does not take place in the hyperbolic plane.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Thong:2006:CFG,
  author =       "Nguyen Quang Do Thong",
  title =        "Sur la conjecture faible de {Greenberg} dans le cas
                 ab{\'e}lien $p$-d{\'e}compos{\'e}. ({French}) [{On} the
                 weak conjecture of {Greenberg} in the abelian
                 $p$-decomposed case]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "49--64",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000395",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000395",
  abstract =     "Let p be an odd prime. For any CM number field K
                 containing a primitive pth root of unity, class field
                 theory and Kummer theory put together yield the well
                 known reflection inequality \lambda$^+$ \leq
                 \lambda$^-$ between the ``plus'' and ``minus'' parts of
                 the \lambda -invariant of K. Greenberg's classical
                 conjecture predicts the vanishing of \lambda$^+$. We
                 propose a weak form of this conjecture: \lambda$^+$ =
                 \lambda$^-$ if and only if \lambda$^+$ = \lambda$^-$ =
                 0, and we prove it when K$^+$ is abelian, p is totally
                 split in K$^+$, and certain conditions on the
                 cohomology of circular units are satisfied (e.g. in the
                 semi-simple case).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Borwein:2006:TTG,
  author =       "Jonathan M. Borwein and David M. Bradley",
  title =        "Thirty-two {Goldbach} variations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "65--103",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000383",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11M41 (11M06)",
  MRnumber =     "2217795",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/301/;
                 https://www.worldscientific.com/doi/10.1142/S1793042106000383",
  abstract =     "We give thirty-two diverse proofs of a small
                 mathematical gem --- the fundamental Euler sum identity
                 $ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar {2}, 1) $.
                 We also discuss various generalizations for multiple
                 harmonic (Euler) sums and some of their many
                 connections, thereby illustrating both the wide variety
                 of techniques fruitfully used to study such sums and
                 the attraction of their study.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2006:TTG",
}

@Article{Chan:2006:NPS,
  author =       "Tsz Ho Chan",
  title =        "A Note on Primes in Short Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "105--110",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000437",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000437",
  abstract =     "Montgomery and Soundararajan obtained evidence for the
                 Gaussian distribution of primes in short intervals
                 assuming a quantitative Hardy--Littlewood conjecture.
                 In this article, we show that their methods may be
                 modified and an average form of the Hardy--Littlewood
                 conjecture suffices.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Takloo-Bighash:2006:RPA,
  author =       "Ramin Takloo-Bighash",
  title =        "A Remark on a Paper of {Ahlgren}, {Berndt}, {Yee}, and
                 {Zaharescu}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "111--114",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000450",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000450",
  abstract =     "A classical theorem of Ramanujan relates an integral
                 of Dedekind eta-function to a special value of a
                 Dirichlet {$L$}-function at s = 2. Ahlgren, Berndt, Yee
                 and Zaharescu have generalized this result [1]. In this
                 paper, we generalize this result to the context of
                 holomorphic cusp forms on the upper half space.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cooper:2006:QPI,
  author =       "Shaun Cooper",
  title =        "The Quintuple Product Identity",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "115--161",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000401",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000401",
  abstract =     "The quintuple product identity was first discovered
                 about 90 years ago. It has been published in many
                 different forms, and at least 29 proofs have been
                 given. We shall give a comprehensive survey of the work
                 on the quintuple product identity, and a detailed
                 analysis of the many proofs.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{El-Mahassni:2006:DNC,
  author =       "Edwin D. El-Mahassni and Arne Winterhof",
  title =        "On the Distribution of Nonlinear Congruential
                 Pseudorandom Numbers in Residue Rings",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "163--168",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000413",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000413",
  abstract =     "The nonlinear congruential method is an attractive
                 alternative to the classical linear congruential method
                 for pseudorandom number generation. In this paper we
                 present a new type of discrepancy bound for sequences
                 of s-tuples of successive nonlinear congruential
                 pseudorandom numbers over a ring of integers
                 {\mathbb{Z}}$_M$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Walling:2006:AHO,
  author =       "Lynne H. Walling",
  title =        "Action of {Hecke} Operators on {Siegel} Theta Series
                 {I}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "169--186",
  month =        jun,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042106000516",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000516",
  abstract =     "We apply the Hecke operators T(p) and to a degree n
                 theta series attached to a rank 2k {\mathbb{Z}}-lattice
                 L, n \leq k, equipped with a positive definite
                 quadratic form in the case that L/pL is hyperbolic. We
                 show that the image of the theta series under these
                 Hecke operators can be realized as a sum of theta
                 series attached to certain closely related lattices,
                 thereby generalizing the Eichler Commutation Relation
                 (similar to some work of Freitag and of Yoshida). We
                 then show that the average theta series (averaging over
                 isometry classes in a given genus) is an eigenform for
                 these operators. We show the eigenvalue for T(p) is \in
                 (k - n, n), and the eigenvalue for T\prime$_j$ (p$^2$)
                 (a specific linear combination of T$_0$ (p$^2$),\ldots,
                 T$_j$ (p$^2$)) is p$^{j(k - n) + j(j - 1) / 2}$ \beta
                 (n,j)\in (k-j,j) where \beta (*,*), \in (*,*) are
                 elementary functions (defined below).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bringmann:2006:BBA,
  author =       "Kathrin Bringmann and Benjamin Kane and Winfried
                 Kohnen",
  title =        "On the Boundary Behavior of Automorphic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "187--194",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000565",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000565",
  abstract =     "We investigate the boundary behavior of modular forms
                 f on the full modular group. We first show that $ \{ x
                 \in [0, 1] | \lim_{y \rightarrow 0^+} y^{k / 2} |f(x +
                 i y)| \mathrm {exists} \} $ is contained in a set of
                 Lebesgue measure 0. In particular, we recover the
                 well-known fact that the real axis is a natural
                 boundary of definition for f. On the other hand, using
                 the Rankin--Selberg Dirichlet series attached to f, we
                 show that taking the limit over the ``average'' over
                 all x \in [0,1] behaves ``well''. Our results also
                 apply to Maass wave forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bennett:2006:GTB,
  author =       "Michael A. Bennett and Alain Togb{\'e} and P. G.
                 Walsh",
  title =        "A Generalization of a Theorem of {Bumby} on Quartic
                 {Diophantine} Equations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "195--206",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000474",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000474",
  abstract =     "Bumby proved that the only positive integer solutions
                 to the quartic Diophantine equation 3X$^4$- 2Y$^2$ = 1
                 are (X, Y) = (1, 1),(3, 11). In this paper, we use
                 Thue's hypergeometric method to prove that, for each
                 integer m \geq 1, the only positive integers solutions
                 to the Diophantine equation (m$^2$ + m + 1)X$^4$-
                 (m$^2$ + m)Y$^2$ = 1 are (X,Y) = (1, 1),(2m + 1, 4m$^2$
                 + 4m + 3).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Laishram:2006:GCC,
  author =       "Shanta Laishram and T. N. Shorey",
  title =        "{Grimm}'s Conjecture on Consecutive Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "207--211",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000498",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000498",
  abstract =     "For positive integers n and k, it is possible to
                 choose primes P$_1$, P$_2$, \ldots, P$_k$ such that
                 P$_i$ | (n + i) for 1 \leq i \leq k whenever n + 1, n +
                 2,\ldots, n + k are all composites and n \leq 1.9 $
                 \times $ 10$^{10}$. This provides a numerical
                 verification of Grimm's Conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hirschhorn:2006:CMS,
  author =       "Michael D. Hirschhorn",
  title =        "The Case of the Mysterious Sevens",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "213--216",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000486",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000486",
  abstract =     "We give a simple, direct proof of a theorem involving
                 partitions into distinct parts, where multiples of 7
                 come in two colours.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bremner:2006:TRP,
  author =       "Andrew Bremner and Richard K. Guy",
  title =        "Triangle-Rectangle Pairs with a Common Area and a
                 Common Perimeter",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "217--223",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000504",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000504",
  abstract =     "We solve a problem of Bill Sands, to find pairs of
                 Heron triangles and rectangles, such as (5,5,6) & [2 $
                 \times $ 6] or (13,20,21) & [6 $ \times $ 21] which
                 have a common area and a common perimeter. The original
                 question was posed for right-angled triangles, but
                 there are no nondegenerate such. There are infinitely
                 many isosceles triangles and these have been exhibited
                 by Guy. Here we solve the general problem; the
                 triangle-rectangle pairs are parametrized by a family
                 of elliptic curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Tolev:2006:DTS,
  author =       "D. I. Tolev",
  title =        "On the distribution of $r$-tuples of squarefree
                 numbers in short intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "225--234",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S179304210600053X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210600053X",
  abstract =     "We consider the number of r-tuples of squarefree
                 numbers in a short interval. We prove that it cannot be
                 much bigger than the expected value and we also
                 establish an asymptotic formula if the interval is not
                 very short.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Spearman:2006:DCC,
  author =       "Blair K. Spearman and Kenneth S. Williams",
  title =        "On the Distribution of Cyclic Cubic Fields with Index
                 $2$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "235--247",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000541",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000541",
  abstract =     "In this paper we prove an analogue of Mertens' theorem
                 for primes of each of the forms a$^2$ +27b$^2$ and
                 4a$^2$ +2ab+7b$^2$ and then use this result to
                 determine an asymptotic formula for the number of
                 positive integers n \leq x which are discriminants of
                 cyclic cubic fields with each such field having field
                 index 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Grekos:2006:VTC,
  author =       "G. Grekos and L. Haddad and C. Helou and J. Pihko",
  title =        "Variations on a Theme of {Cassels} for Additive
                 Bases",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "249--265",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000553",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000553",
  abstract =     "We introduce the notion of caliber, cal(A, B), of a
                 strictly increasing sequence of natural numbers A with
                 respect to another one B, as the limit inferior of the
                 ratio of the nth term of A to that of B. We further
                 consider the limit superior t(A) of the average order
                 of the number of representations of an integer as a sum
                 of two elements of A. We give some basic properties of
                 each notion and we relate the two together, thus
                 yielding a generalization, of the form t(A) \leq
                 t(B)/cal(A, B), of a result of Cassels specific to the
                 case where A is an additive basis of the natural
                 numbers and B is the sequence of perfect squares. We
                 also provide some formulas for the computation of t(A)
                 in a large class of cases, and give some examples.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kowalski:2006:RQT,
  author =       "E. Kowalski",
  title =        "On the Rank of Quadratic Twists of Elliptic Curves
                 Over Function Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "267--288",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000528",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000528",
  abstract =     "We prove quantitative upper bounds for the number of
                 quadratic twists of a given elliptic curve E/F$_q$ (C)
                 over a function field over a finite field that have
                 rank \geq 2, and for their average rank. The main tools
                 are constructions and results of Katz and uniform
                 versions of the Chebotarev density theorem for
                 varieties over finite fields. Moreover, we
                 conditionally derive a bound in some cases where the
                 degree of the conductor is unbounded.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gaborit:2006:ELG,
  author =       "Philippe Gaborit and Ann Marie Natividad and Patrick
                 Sol{\'e}",
  title =        "{Eisenstein} Lattices, {Galois} Rings and Quaternary
                 Codes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "289--303",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000577",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000577",
  abstract =     "Self-dual codes over the Galois ring GR(4,2) are
                 investigated. Of special interest are quadratic double
                 circulant codes. Euclidean self-dual (Type II) codes
                 yield self-dual (Type II) {\mathbb{Z}}$_4$-codes by
                 projection on a trace orthogonal basis. Hermitian
                 self-dual codes also give self-dual {\mathbb{Z}}$_4$
                 codes by the cubic construction, as well as Eisenstein
                 lattices by Construction A. Applying a suitable Gray
                 map to self-dual codes over the ring gives formally
                 self-dual {$ \mathbb {F} $}$_4$-codes, most notably in
                 length 12 and 24. Extremal unimodular lattices in
                 dimension 38, 42 and the first extremal 3-modular
                 lattice in dimension 44 are constructed.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Loh:2006:ACP,
  author =       "Po-Ru Loh and Robert C. Rhoades",
  title =        "$p$-adic and combinatorial properties of modular form
                 coefficients",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "2",
  pages =        "305--328",
  month =        jun,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000590",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000590",
  abstract =     "For two particular classes of elliptic curves, we
                 establish congruences relating the coefficients of
                 their corresponding modular forms to combinatorial
                 objects. These congruences resemble a supercongruence
                 for the Ap{\'e}ry numbers conjectured by Beukers and
                 proved by Ahlgren and Ono in [1]. We also consider the
                 trace Tr$_{2k}$ (\Gamma$_0$ (N), n) of the Hecke
                 operator T$_n$ acting on the space of cusp forms
                 S$_{2k}$ (\Gamma$_0$ (N)). We show that for (n, N) = 1,
                 these traces interpolate $p$-adically in the weight
                 aspect.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Flicker:2006:TCS,
  author =       "Yuval Z. Flicker and Dmitrii Zinoviev",
  title =        "Twisted Character of a Small Representation of {$
                 \mathrm {Gl}(4) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "329--350",
  month =        sep,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042106000589",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000589",
  abstract =     "We compute by a purely local method the (elliptic) $
                 \theta $-twisted character $ \chi_{\pi Y}$ of the
                 representation \pi_Y = I_{(3, 1)} (1_3 \times \chi_Y)
                 of G = GL(4, F), where F is a $p$-adic field, p \neq 2,
                 and Y is an unramified quadratic extension of F; \chi_Y
                 is the nontrivial character of F^{\times} /N_{Y/F}
                 Y^{\times}. The representation \pi_Y is normalizedly
                 induced from, m_i \in GL(i, F), on the maximal
                 parabolic subgroup of type (3, 1); \theta is the
                 ``transpose-inverse'' involution of G. We show that the
                 twisted character \chi_{\pi Y} of \pi_Y is an unstable
                 function: its value at a twisted regular elliptic
                 conjugacy class with norm in C_Y = C_Y (F)=``(GL(2,
                 Y)/F^{\times})_F is minus its value at the other class
                 within the twisted stable conjugacy class. It is 0 at
                 the classes without norm in C_Y. Moreover \pi_Y is the
                 endoscopic lift of the trivial representation of C_Y.
                 We deal only with unramified Y/F, as globally this case
                 occurs almost everywhere. The case of ramified Y/F
                 would require another paper. Our C_Y = ``(R_{Y/F}
                 GL(2)/GL(1))_F '' has Y-points C_Y (Y) = {(g, g\prime)
                 \in GL(2, Y) \times GL(2, Y); det(g) =
                 det(g\prime)}/Y^{\times} (Y^{\times} embeds
                 diagonally); \sigma(\neq 1) in Gal(Y/F) acts by \sigma
                 (g, g\prime) = (\sigma g\prime, \sigma g). It is a
                 \theta -twisted elliptic endoscopic group of GL(4).
                 Naturally this computation plays a role in the theory
                 of lifting of C_Y and GSp(2) to GL(4) using the trace
                 formula, to be discussed elsewhere. Our work extends
                 --- to the context of nontrivial central characters ---
                 the work of [7], where representations of PGL(4, F) are
                 studied. In [7] we develop a 4-dimensional analogue of
                 the model of the small representation of PGL(3, F)
                 introduced by the first author and Kazhdan in [5] in a
                 3-dimensional case, and we extend the local method of
                 computation introduced in [6]. As in [7] we use here
                 the classification of twisted (stable) regular
                 conjugacy classes in GL(4, F) of [4], motivated by
                 Weissauer [13].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baoulina:2006:EFF,
  author =       "Ioulia Baoulina",
  title =        "On the Equation Over a Finite Field",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "351--363",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000607",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000607",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hbaib:2006:BDC,
  author =       "M. Hbaib and M. Mkaouar",
  title =        "Sur le b{\^e}ta-d{\'e}veloppement de $1$ dans le corps
                 des s{\'e}ries formelles. ({French}) [{On} the
                 beta-development of $1$ in the body of formal series]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "365--378",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000619",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000619",
  abstract =     "Let \beta be a fixed element of {$ \mathbb {F} $}$_q$
                 ((X$^{-1}$)) with polynomial part of degree \geq 1,
                 then any formal power series can be represented in base
                 \beta, using the transformation T$_{\beta }$: f \mapsto
                 {\beta f} of the unit disk. Any formal power series in
                 is expanded in this way into d$_{\beta }$ (f) = (a$_i$
                 (X))$_{i \geq 1}$, where. The main aim of this paper is
                 to characterize the formal power series \beta (|\beta |
                 > 1), such that d$_{\beta }$ (1) is finite, eventually
                 periodic or automatic (such characterizations do not
                 exist in the real case).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Lev:2006:CPA,
  author =       "Vsevolod F. Lev",
  title =        "Critical Pairs in {Abelian} Groups and {Kemperman}'s
                 Structure Theorem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "379--396",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000620",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000620",
  abstract =     "A well-known result by Kemperman describes the
                 structure of those pairs (A, B) of finite subsets of an
                 abelian group satisfying |A + B| \leq |A| + |B| -1. We
                 establish a description which is, in a sense, dual to
                 Kemperman's, and as an application sharpen several
                 results due to Deshouillers, Hamidoune, Hennecart, and
                 Plagne.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Movasati:2006:HSH,
  author =       "H. Movasati and S. Reiter",
  title =        "Hypergeometric Series and {Hodge} Cycles of Four
                 Dimensional Cubic Hypersurfaces",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "397--416",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000632",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000632",
  abstract =     "In this article we find connections between the values
                 of Gauss hypergeometric functions and the dimension of
                 the vector space of Hodge cycles of four-dimensional
                 cubic hypersurfaces. Since the Hodge conjecture is
                 well-known for those varieties we calculate values of
                 hypergeometric series on certain CM points. Our methods
                 are based on the calculation of the Picard--Fuchs
                 equations in higher dimensions, reducing them to the
                 Gauss equation and then applying the Abelian Subvariety
                 Theorem to the corresponding hypergeometric abelian
                 varieties.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Matala-Aho:2006:VCF,
  author =       "Tapani Matala-Aho and Ville Meril{\"a}",
  title =        "On the values of continued fractions: $q$-series
                 {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "417--430",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000656",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000656",
  abstract =     "Let polynomials $ S(t) $, $ T(t) $ be given, then the
                 convergence of the $q$-continued fraction $ T(t) +
                 \mathbb {K}_{n = 1}^\infty \frac {S(t q^{n - 1})}{T(t
                 q^n)}$ will be studied using the Poincar{\'e}--Perron
                 Theorem and Frobenius series solutions of the
                 corresponding q-difference equation $ S(t) H(q^2 t) =
                 T(t) H(q t) + H(t)$. Our applications include a
                 generalization of a $q$-continued fraction identity of
                 Ramanujan and certain $q$-fractions, which arise in the
                 theory of $q$-orthogonal polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dodson:2006:KTT,
  author =       "M. M. Dodson and S. Kristensen",
  title =        "{Khintchine}'s Theorem and Transference Principle for
                 Star Bodies",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "431--453",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000668",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000668",
  abstract =     "Analogues of Khintchine's Theorem in simultaneous
                 Diophantine approximation in the plane are proved with
                 the classical height replaced by fairly general planar
                 distance functions or equivalently star bodies.
                 Khintchine's transference principle is discussed for
                 distance functions and a direct proof for the
                 multiplicative version is given. A transference
                 principle is also established for a different distance
                 function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rodseth:2006:PPF,
  author =       "{\O}ystein J. R{\o}dseth and James A. Sellers",
  title =        "Partitions with Parts in a Finite Set",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "3",
  pages =        "455--468",
  month =        sep,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000644",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:14 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000644",
  abstract =     "For a finite set A of positive integers, we study the
                 partition function p$_A$ (n). This function enumerates
                 the partitions of the positive integer n into parts in
                 A. We give simple proofs of some known and unknown
                 identities and congruences for p$_A$ (n). For n in a
                 special residue class, p$_A$ (n) is a polynomial in n.
                 We examine these polynomials for linear factors, and
                 the results are applied to a restricted m-ary partition
                 function. We extend the domain of p$_A$ and prove a
                 reciprocity formula with supplement. In closing we
                 consider an asymptotic formula for p$_A$ (n) and its
                 refinement.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nicolas:2006:VIF,
  author =       "Jean-Louis Nicolas",
  title =        "Valeurs impaires de la fonction de partition $ p(n) $.
                 ({French}) [{Odd} values of the partition function $
                 p(n) $]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "469--487",
  month =        dec,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S179304210600067X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210600067X",
  abstract =     "Let p(n) denote the number of partitions of n, and for
                 i = 0 (resp. 1), A$_i$ (x) denote the number of n \leq
                 x such that p(n) is even (resp. odd). In this paper, it
                 is proved that for some constant K > 0, holds for x
                 large enough. This estimation slightly improves a
                 preceding result of S. Ahlgren who obtained the above
                 lower bound for K = 0. Let and ; the main tool is a
                 result of J.-P. Serre about the distribution of odd
                 values of \tau$_k$ (n). Effective lower bounds for
                 A$_0$ (x) and A$_1$ (x) are also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Ayuso:2006:NST,
  author =       "Pedro Fortuny Ayuso and Fritz Schweiger",
  title =        "A New Symmetric Two-Dimensional Algorithm",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "489--498",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000681",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000681",
  abstract =     "Continued fractions are deeply related to Singularity
                 Theory, as the computation of the Puiseux exponents of
                 a plane curve from its dual graph clearly shows.
                 Another closely related topic is Euclid's Algorithm for
                 computing the gcd of two integers (see [2] for a
                 detailed overview). In the first section, we describe a
                 subtractive algorithm for computing the gcd of n
                 integers, related to singularities of curves in affine
                 n-space. This gives rise to a multidimensional
                 continued fraction algorithm whose version in dimension
                 2 is the main topic of the paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cooper:2006:RBP,
  author =       "Joshua N. Cooper and Dennis Eichhorn and Kevin
                 O'Bryant",
  title =        "Reciprocals of Binary Power Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "499--522",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000693",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000693",
  abstract =     "If A is a set of nonnegative integers containing 0,
                 then there is a unique nonempty set B of nonnegative
                 integers such that every positive integer can be
                 written in the form a + b, where a \in A and b \in B,
                 in an even number of ways. We compute the natural
                 density of B for several specific sets A, including the
                 Prouhet--Thue--Morse sequence, {0} \cup {2$^n$ :n \in
                 \mathbb{N} }, and random sets, and we also study the
                 distribution of densities of B for finite sets A. This
                 problem is motivated by Euler's observation that if A
                 is the set of n that has an odd number of partitions,
                 then B is the set of pentagonal numbers {n(3n + 1)/2:n
                 \in {\mathbb{Z}}}. We also elaborate the connection
                 between this problem and the theory of de Bruijn
                 sequences and linear shift registers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bowman:2006:CF,
  author =       "D. Bowman and J. McLaughlin and N. J. Wyshinski",
  title =        "A $q$-continued fraction",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "523--547",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S179304210600070X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210600070X",
  abstract =     "We use the method of generating functions to find the
                 limit of a q-continued fraction, with 4 parameters, as
                 a ratio of certain $q$-series. We then use this result
                 to give new proofs of several known continued fraction
                 identities, including Ramanujan's continued fraction
                 expansions for (q$^2$; q$^3$)$_{\infty }$ /(q;
                 q$^3$)$_{\infty }$ and. In addition, we give a new
                 proof of the famous Rogers--Ramanujan identities. We
                 also use our main result to derive two generalizations
                 of another continued fraction due to Ramanujan.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gun:2006:TZC,
  author =       "Sanoli Gun",
  title =        "Transcendental Zeros of Certain Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "549--553",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000711",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000711",
  abstract =     "Kohnen showed that the zeros of the Eisenstein series
                 E$_k$ in the standard fundamental domain other than i
                 and \rho are transcendental. In this paper, we obtain
                 similar results for a more general class of modular
                 forms, using the earlier works of Kanou, Kohnen and the
                 recent work of Getz.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pontreau:2006:GLB,
  author =       "Corentin Pontreau",
  title =        "Geometric Lower Bounds for the Normalized Height of
                 Hypersurfaces",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "555--568",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000723",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000723",
  abstract =     "Here we are concerned on Bogomolov's problem for
                 hypersurfaces; we give a geometric lower bound for the
                 height of a hypersurface of (i.e. without condition on
                 the field of definition of the hypersurface) which is
                 not a translate of an algebraic subgroup of . This is
                 an analogue of a result of F. Amoroso and S. David who
                 give a lower bound for the height of non-torsion
                 hypersurfaces defined and irreducible over the
                 rationals.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jadrijevic:2006:SRP,
  author =       "Borka Jadrijevi{\'c} and Volker Ziegler",
  title =        "A System of Relative {Pellian} Equations and a Related
                 Family of Relative {Thue} Equations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "569--590",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000735",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000735",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Byard:2006:QRD,
  author =       "Kevin Byard",
  title =        "On Qualified Residue Difference Sets",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "591--597",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000747",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000747",
  abstract =     "Qualified residue difference sets of power n are known
                 to exist for n = 2,4,6, as do similar sets that include
                 the zero element. Both classes of sets are proved
                 non-existent for n = 8.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kanemitsu:2006:SNT,
  author =       "Shigeru Kanemitsu and Yoshio Tanigawa and Haruo
                 Tsukada",
  title =        "Some Number Theoretic Applications of a General
                 Modular Relation",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "599--615",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000759",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000759",
  abstract =     "We state a form of the modular relation in which the
                 functional equation appears in the form of an
                 expression of one Dirichlet series in terms of the
                 other multiplied by the quotient of gamma functions and
                 illustrate it by some concrete examples including the
                 results of Koshlyakov, Berndt and Wigert and Bellman.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2006:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 2)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "4",
  pages =        "617--619",
  month =        dec,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000760",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042106000760",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Granville:2007:PDP,
  author =       "Andrew Granville",
  title =        "Prime Divisors Are {Poisson} Distributed",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "1--18",
  month =        mar,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042107000778",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See erratum \cite{Granville:2007:EPD}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000778",
  abstract =     "We show that the set of prime factors of almost all
                 integers are ``Poisson distributed'', and that this
                 remains true (appropriately formulated) even when we
                 restrict the number of prime factors of the integer.
                 Our results have inspired analogous results about the
                 distribution of cycle lengths of permutations.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Angles:2007:RI,
  author =       "Bruno Angl{\`e}s and Thomas Herreng",
  title =        "On a Result of {Iwasawa}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "19--41",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000791",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000791",
  abstract =     "We recover a result of Iwasawa on the $p$-adic
                 logarithm of principal units of {$ \mathbb
                 {Q}_p(\zeta_{p^{n + 1}})$} by studying the value at s =
                 1 of $p$-adic {$L$}-functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Garvan:2007:SSP,
  author =       "Frank G. Garvan and Hamza Yesilyurt",
  title =        "Shifted and Shiftless Partition Identities {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "43--84",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000808",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000808",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dilcher:2007:PAS,
  author =       "Karl Dilcher and Kenneth B. Stolarsky",
  title =        "A Polynomial Analogue to the {Stern} Sequence",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "85--103",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S179304210700081X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210700081X",
  abstract =     "We extend the Stern sequence, sometimes also called
                 Stern's diatomic sequence, to polynomials with
                 coefficients 0 and 1 and derive various properties,
                 including a generating function. A simple iteration for
                 quotients of consecutive terms of the Stern sequence,
                 recently obtained by Moshe Newman, is extended to this
                 polynomial sequence. Finally we establish connections
                 with Stirling numbers and Chebyshev polynomials,
                 extending some results of Carlitz. In the process we
                 also obtain some new results and new proofs for the
                 classical Stern sequence.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Choi:2007:CSP,
  author =       "H. Timothy Choi and Ronald Evans",
  title =        "Congruences for Sums of Powers of {Kloosterman} Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "105--117",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000821",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000821",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Shevelev:2007:D,
  author =       "Vladimir Shevelev",
  title =        "On divisibility of $ \binom {n - i - 1}{i - 1} $ by
                 $i$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "119--139",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S179304210700078X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210700078X",
  abstract =     "We investigate the function b(n) = \sum 1, where the
                 summing is over all i for which.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hart:2007:NCM,
  author =       "William B. Hart",
  title =        "A New Class of Modular Equation for {Weber}
                 Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "141--157",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000845",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000845",
  abstract =     "We describe the construction of a new type of modular
                 equation for Weber functions. These bear some
                 relationship to Weber's modular equations of the {\em
                 irrational kind}. Numerous examples of these
                 equations are explicitly computed. We also obtain some
                 modular equations of the irrational kind which are not
                 present in Weber's work.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Croot:2007:SNS,
  author =       "Ernie Croot",
  title =        "Smooth Numbers in Short Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "1",
  pages =        "159--169",
  month =        mar,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000833",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000833",
  abstract =     "We show that for any \in > 0, there exists c > 0, such
                 that for all x sufficiently large, there are x$^{1 /
                 2}$ (log x)$^{-log 4 - o(1)}$ integers, all of whose
                 prime factors are.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Wittmann:2007:PDC,
  author =       "Christian Wittmann",
  title =        "$l$-parts of divisor class groups of cyclic function
                 fields of degree $l$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "171--190",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042107000857",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000857",
  abstract =     "Let l be a prime number and K be a cyclic extension of
                 degree l of the rational function field {$ \mathbb {F}
                 $}$_q$ (T) over a finite field of characteristic \neq =
                 l. Using class field theory we investigate the l-part
                 of Pic$^0$ (K), the group of divisor classes of degree
                 0 of K, considered as a Galois module. In particular we
                 give deterministic algorithms that allow the
                 computation of the so-called (\sigma - 1)-rank and the
                 (\sigma - 1)$^2$-rank of Pic$^0$ (K), where \sigma
                 denotes a generator of the Galois group of K/{$ \mathbb
                 {F} $}$_q$ (T). In the case l = 2 this yields the exact
                 structure of the 2-torsion and the 4-torsion of Pic$^0$
                 (K) for a hyperelliptic function field K (and hence of
                 the {$ \mathbb {F} $}$_q$-rational points on the
                 Jacobian of the corresponding hyperelliptic curve over
                 {$ \mathbb {F} $}$_q$). In addition we develop similar
                 results for l-parts of S-class groups, where S is a
                 finite set of places of K. In many cases we are able to
                 prove that our algorithms run in polynomial time.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sole:2007:MFC,
  author =       "Patrick Sol{\'e} and Dmitrii Zinoviev",
  title =        "A {Macwilliams} Formula for Convolutional Codes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "191--206",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000869",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000869",
  abstract =     "Regarding convolutional codes as polynomial analogues
                 of arithmetic lattices, we derive a Poisson--Jacobi
                 formula for their trivariate weight enumerator. The
                 proof is based on harmonic analysis on locally compact
                 abelian groups as developed in Tate's thesis to derive
                 the functional equation of the zeta function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alkan:2007:ASG,
  author =       "Emre Alkan",
  title =        "Average Size of Gaps in the {Fourier} Expansion of
                 Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "207--215",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000870",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000870",
  abstract =     "We prove that certain powers of the gap function for
                 the newform associated to an elliptic curve without
                 complex multiplication are ``finite'' on average. In
                 particular we obtain quantitative results on the number
                 of large values of the gap function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Amoroso:2007:MPE,
  author =       "Francesco Amoroso",
  title =        "Une minoration pour l'exposant du groupe des classes
                 d'un corps engendr{\'e} par un nombre de {Salem}.
                 ({French}) [{A} lower bound for the exponent of the
                 group of classes of a field generated by a number of
                 {Salem}]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "217--229",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000882",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000882",
  abstract =     "In this article we extend the main result of [2]
                 concerning lower bounds for the exponent of the class
                 group of CM-fields. We consider a number field K
                 generated by a Salem number \alpha. If k denotes the
                 field fixed by \alpha \mapsto \alpha$^{-1}$ we prove,
                 under the generalized Riemann hypothesis for the
                 Dedekind zeta function of K, lower bounds for the
                 relative exponent e$_{K / k}$ and the relative size
                 h$_{K / k}$ of the class group of K with respect to the
                 class group of k.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Royer:2007:ECS,
  author =       "Emmanuel Royer",
  title =        "Evaluating Convolution Sums of the Divisor Function by
                 Quasimodular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "231--261",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000924",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000924",
  abstract =     "We provide a systematic method to compute arithmetic
                 sums including some previously computed by Alaca,
                 Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi,
                 Ou, Ramanujan, Spearman and Williams. Our method is
                 based on quasimodular forms. This extension of modular
                 forms has been constructed by Kaneko and Zagier.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mukhopadhyay:2007:ZDE,
  author =       "Anirban Mukhopadhyay and Kotyada Srinivas",
  title =        "A Zero Density Estimate for the {Selberg} Class",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "263--273",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000894",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000894",
  abstract =     "It is well known that bounds on moments of a specific
                 {$L$}-function can lead to zero-density result for that
                 {$L$}-function. In this paper, we generalize this
                 argument to all {$L$}-functions in the Selberg class by
                 assuming a certain second power moment. As an
                 application, it is shown that in the case of
                 symmetric-square {$L$}-function, this result improves
                 the existing one.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{VanWamelen:2007:NEM,
  author =       "Paul {Van Wamelen}",
  title =        "New Explicit Multiplicative Relations Between {Gauss}
                 Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "275--292",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000900",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000900",
  abstract =     "We study multiplicative identities between Gauss sums.
                 If such an identity does not follow from the
                 Davenport--Hasse relation and the norm relation, it is
                 called a sign ambiguity. Until recently only a finite
                 number of explicit sign ambiguities were known. We
                 generalize the first infinite family of sign
                 ambiguities as found by Murray.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sills:2007:IRR,
  author =       "Andrew V. Sills",
  title =        "Identities of the {Rogers--Ramanujan--Slater} Type",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "293--323",
  month =        jun,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000912",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:15 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000912",
  abstract =     "It is shown that (two-variable generalizations of)
                 more than half of Slater's list of 130
                 Rogers--Ramanujan identities (L. J. Slater, Further
                 identities of the Rogers--Ramanujan type, {\em Proc.
                 London Math Soc. (2)\/} 54 (1952) 147--167) can be
                 easily derived using just three multiparameter Bailey
                 pairs and their associated q-difference equations. As a
                 bonus, new Rogers--Ramanujan type identities are found
                 along with natural combinatorial interpretations for
                 many of these identities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2007:P,
  author =       "Anonymous",
  title =        "Preface",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "v--vi",
  month =        sep,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042107001061",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001061",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Andrews:2007:FD,
  author =       "George E. Andrews",
  title =        "A {Fine} Dream",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "325--334",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000948",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000948",
  abstract =     "We shall develop further N. J. Fine's theory of three
                 parameter non-homogeneous first order q-difference
                 equations. The object of our work is to bring the
                 Rogers--Ramanujan identities within the purview of such
                 a theory. In addition, we provide a number of new
                 identities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{DeAzevedoPribitkin:2007:UPS,
  author =       "Wladimir {De Azevedo Pribitkin}",
  title =        "Uninhibited {Poincar{\'e}} Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "335--347",
  month =        sep,
  year =         "2007",
  DOI =          "",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210700095X",
  abstract =     "We introduce a class of functions that generalize the
                 epoch-making series of Poincar{\'e} and Petersson. Our
                 ``uninhibited Poincar{\'e} series'' permits both a
                 complex weight and an arbitrary multiplier system that
                 is independent of the weight. In this initial paper we
                 provide their Fourier expansions, as well as their
                 modular behavior. We show that they are modular
                 integrals that possess interesting periods. Moreover,
                 we establish with relative ease that they ``almost
                 never'' vanish identically. Along the way we present a
                 seemingly unknown historical truth concerning
                 Kloosterman sums, and also an alternative approach to
                 Petersson's factor systems. The latter depends upon a
                 simple multiplication rule.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Berndt:2007:RCP,
  author =       "Bruce C. Berndt",
  title =        "{Ramanujan}'s Congruences for the Partition Function
                 Modulo $5$, $7$, and $ 11$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "349--354",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000961",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000961",
  abstract =     "Using Ramanujan's differential equations for
                 Eisenstein series and an idea from Ramanujan's
                 unpublished manuscript on the partition function p(n)
                 and the tau function \tau (n), we provide simple proofs
                 of Ramanujan's congruences for p(n) modulo 5, 7, and
                 11.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Iwaniec:2007:FNH,
  author =       "H. Iwaniec and W. Kohnen and J. Sengupta",
  title =        "The First Negative {Hecke} Eigenvalue",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "355--363",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001024",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001024",
  abstract =     "We shall improve earlier estimates on the first sign
                 change of the Hecke eigenvalues of a normalized
                 cuspidal newform of level N.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Goldfeld:2007:RLO,
  author =       "Dorian Goldfeld",
  title =        "Rank lowering operators on {$ \mathrm {GL}(n, \mathbb
                 {R}) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "365--375",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000985",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000985",
  abstract =     "If one takes the Mellin transform of an automorphic
                 form for GL(n) and then integrates it along the
                 diagonal on GL(n - 1) then one obtains an automorphic
                 form on GL(n - 1). This gives a rank lowering operator.
                 In this paper a more general rank lowering operator is
                 obtained by combining the Mellin transform with a sum
                 of powers of certain fixed differential operators. The
                 analytic continuation of the rank lowering operator is
                 obtained by showing that the spectral expansion
                 consists of sums of Rankin--Selberg {$L$}-functions of
                 type GL(n) $ \times $ GL(n - 1).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mason:2007:VVM,
  author =       "Geoffrey Mason",
  title =        "Vector-Valued Modular Forms and Linear Differential
                 Operators",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "377--390",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000973",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000973",
  abstract =     "We consider holomorphic vector-valued modular forms F
                 of integral weight k on the full modular group \Gamma =
                 SL(2, {\mathbb{Z}}) corresponding to representations of
                 \Gamma of arbitrary finite dimension p. Assuming that
                 the component functions of F are linearly independent,
                 we prove that the inequality k \geq 1 - p always holds,
                 and that equality holds only in the trivial case when p
                 = 1 and k = 0. For any p \geq 2, we show how to
                 construct large numbers of representations of \Gamma
                 for which k = 2 - p. The key idea is to consider
                 representations of \Gamma on spaces of solutions of
                 certain linear differential equations whose
                 coefficients are modular forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Caulk:2007:HOH,
  author =       "Suzanne Caulk and Lynne H. Walling",
  title =        "{Hecke} Operators on {Hilbert--Siegel} Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "391--420",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001048",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001048",
  abstract =     "We define Hilbert--Siegel modular forms and Hecke
                 ``operators'' acting on them. As with Hilbert modular
                 forms (i.e. with Siegel degree 1), these linear
                 transformations are not linear operators until we
                 consider a direct product of spaces of modular forms
                 (with varying groups), modulo natural identifications
                 we can make between certain spaces. With
                 Hilbert--Siegel forms (i.e. with arbitrary Siegel
                 degree) we identify several families of natural
                 identifications between certain spaces of modular
                 forms. We associate the Fourier coefficients of a form
                 in our product space to even integral lattices,
                 independent of basis and choice of coefficient rings.
                 We then determine the action of the Hecke operators on
                 these Fourier coefficients, paralleling the result of
                 Hafner and Walling for Siegel modular forms (where the
                 number field is the field of rationals).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Schmidt:2007:CLH,
  author =       "Thomas A. Schmidt and Mark Sheingorn",
  title =        "Classifying Low Height Geodesics On {$ \Gamma^3
                 \setminus \mathcal {H} $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "421--438",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001012",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001012",
  abstract =     "We show that low height-achieving non-simple geodesics
                 on a low-index cover of the modular surface can be
                 classified into seven types, according to the topology
                 of highest arcs. The lowest geodesics of the signature
                 (0;2,2,2,\infty)-orbifold are the simple closed
                 geodesics; these are indexed up to isometry by Markoff
                 triples of positive integers (x, y, z) with x$^2$ +
                 y$^2$ + z$^2$ = 3xyz, and have heights. Geodesics
                 considered by Crisp and Moran have heights ; they
                 conjectured that these heights, which lie in the
                 ``mysterious region'' between 3 and the Hall ray, are
                 isolated in the Markoff Spectrum. As a step in
                 resolving this conjecture, we characterize the geometry
                 on of geodesic arcs with heights strictly between 3 and
                 6. Of these, one type of geodesic arc cannot realize
                 the height of any geodesic.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hassen:2007:EZF,
  author =       "Abdul Hassen and Hieu D. Nguyen",
  title =        "The Error Zeta Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "439--453",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001000",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001000",
  abstract =     "This paper investigates a new special function
                 referred to as the error zeta function. Derived as a
                 fractional generalization of hypergeometric zeta
                 functions, the error zeta function is shown to exhibit
                 many properties analogous to its hypergeometric
                 counterpart, including its intimate connection to
                 Bernoulli numbers. These new properties are treated in
                 detail and used to demonstrate a pre-functional
                 equation satisfied by this special function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Murty:2007:OVF,
  author =       "M. Ram Murty and V. Kumar Murty",
  title =        "Odd Values of {Fourier} Coefficients of Certain
                 Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "455--470",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001036",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001036",
  abstract =     "Let f be a normalized Hecke eigenform of weight k \ge
                 4 on \Gamma$_0$ (N). Let \lambda$_f$ (n) denote the
                 eigenvalue of the nth Hecke operator acting on f. We
                 show that the number of n such that \lambda$_f$ (n)
                 takes a given value coprime to 2, is finite. We also
                 treat the case of levels 2$^a$ N$_0$ with a arbitrary
                 and N$_0$ = 1, 3, 5, 15 and 17. We discuss the
                 relationship of these results to the classical
                 conjecture of Lang and Trotter.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Choie:2007:RBF,
  author =       "Y. Choie and Y. Chung",
  title =        "Representations of Binary Forms by Quaternary Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "471--474",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000997",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000997",
  abstract =     "In this paper we study a family of quaternary forms
                 which represent almost all binary forms of a certain
                 type. The result follows from the representation number
                 by the genus of ternary forms and a correspondence
                 among theta series.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Schmidt:2007:LHG,
  author =       "Thomas A. Schmidt and Mark Sheingorn",
  title =        "Low Height Geodesics on {$ \Gamma \setminus \mathcal
                 {H} $}: Height Formulas and Examples",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "3",
  pages =        "475--501",
  month =        sep,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S179304210700105X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210700105X",
  abstract =     "The Markoff spectrum of binary indefinite quadratic
                 forms can be studied in terms of heights of geodesics
                 on low-index covers of the modular surface. The lowest
                 geodesics on are the simple closed geodesics; these are
                 indexed up to isometry by Markoff triples of positive
                 integers (x, y, z) with x$^2$ + y$^2$ + z$^2$ = 3xyz,
                 and have heights. Geodesics considered by Crisp and
                 Moran have heights ; they conjectured that these
                 heights, which lie in the ``mysterious region'' between
                 3 and the Hall ray, are isolated in the Markoff
                 Spectrum. In our previous work, we classified the low
                 height-achieving non-simple geodesics of into seven
                 types according to the topology of highest arcs. Here,
                 we obtain explicit formulas for the heights of
                 geodesics of the first three types; the conjecture
                 holds for approximation by closed geodesics of any of
                 these types. Explicit examples show that each of the
                 remaining types is realized.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Eliahou:2007:BMS,
  author =       "Shalom Eliahou and Michel Kervaire",
  title =        "Bounds on the Minimal Sumset Size Function in Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "503--511",
  month =        dec,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042107001085",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001085",
  abstract =     "In this paper, we give lower and upper bounds for the
                 minimal size \mu$_G$ (r,s) of the sumset (or product
                 set) of two finite subsets of given cardinalities r,s
                 in a group G. Our upper bound holds for solvable
                 groups, our lower bound for arbitrary groups. The
                 results are expressed in terms of variants of the
                 numerical function \kappa$_G$ (r,s), a generalization
                 of the Hopf--Stiefel function that, as shown in [6],
                 exactly models \mu$_G$ (r,s) for G abelian.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Evans:2007:RRP,
  author =       "Ronald Evans and Mark {Van Veen}",
  title =        "Rational Representations of Primes by Binary Quadratic
                 Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "513--528",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107000936",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107000936",
  abstract =     "Let q be a positive squarefree integer. A prime p is
                 said to be q-admissible if the equation p = u$^2$ +
                 qv$^2$ has rational solutions u, v. Equivalently, p is
                 q-admissible if there is a positive integer k such
                 that, where is the set of norms of algebraic integers
                 in. Let k(q) denote the smallest positive integer k
                 such that for all q-admissible primes p. It is shown
                 that k(q) has subexponential but suprapolynomial growth
                 in q, as q \rightarrow \infty.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{El-Guindy:2007:LCR,
  author =       "Ahmad El-Guindy",
  title =        "Linear Congruences and Relations on Spaces of Cusp
                 Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "529--539",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001097",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001097",
  abstract =     "Let p be a prime and let f be any cusp form of level l
                 \in {2,3,5,7,13} whose weight satisfy a certain
                 congruence modulo (p-1). Then we exhibit explicit
                 linear combinations of the coefficients of f that must
                 be divisible by p. For a normalized Hecke eigenform,
                 this translates (under mild restrictions) into the pth
                 coefficient itself being divisible by a prime ideal
                 above p in the ring generated by the coefficients of f.
                 This provides many instances of the so-called
                 non-ordinary primes. We also discuss linear relations
                 satisfied universally on the space of modular forms of
                 these levels. These results extend recent work of
                 Choie, Kohnen and Ono in the level 1 case.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2007:FRR,
  author =       "Wai Kiu Chan and A. G. Earnest and Maria Ines Icaza
                 and Ji Young Kim",
  title =        "Finiteness Results for Regular Definite Ternary
                 Quadratic Forms Over",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "541--556",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001103",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001103",
  abstract =     "Let {$ \mathfrak {o} $} be the ring of integers in a
                 number field. An integral quadratic form over {$
                 \mathfrak {o} $} is called regular if it represents all
                 integers in {$ \mathfrak {o} $} that are represented by
                 its genus. In [13,14] Watson proved that there are only
                 finitely many inequivalent positive definite primitive
                 integral regular ternary quadratic forms over
                 {\mathbb{Z}}. In this paper, we generalize Watson's
                 result to totally positive regular ternary quadratic
                 forms over. We also show that the same finiteness
                 result holds for totally positive definite spinor
                 regular ternary quadratic forms over, and thus extends
                 the corresponding finiteness results for spinor regular
                 quadratic forms over {\mathbb{Z}} obtained in [1,3].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pal:2007:EID,
  author =       "Ambrus P{\'a}l",
  title =        "On the {Eisenstein} Ideal of {Drinfeld} Modular
                 Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "557--598",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001115",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001115",
  abstract =     "Let {$ \mathfrak {E} $}({$ \mathfrak {p} $}) denote
                 the Eisenstein ideal in the Hecke algebra {$ \mathbb
                 {T} $}({$ \mathfrak {p} $}) of the Drinfeld modular
                 curve X$_0$ ({$ \mathfrak {p} $}) parameterizing
                 Drinfeld modules of rank two over {$ \mathbb {F} $}$_q$
                 [T] of general characteristic with Hecke level {$
                 \mathfrak {p} $}-structure, where {$ \mathfrak {p} $}
                 \triangleleft {$ \mathbb {F} $}$_q$ [T] is a non-zero
                 prime ideal. We prove that the characteristic p of the
                 field {$ \mathbb {F} $}$_q$ does not divide the order
                 of the quotient {$ \mathbb {T} $}({$ \mathfrak {p}
                 $})/{$ \mathfrak {E} $}({$ \mathfrak {p} $}) and the
                 Eisenstein ideal {$ \mathfrak {E} $}({$ \mathfrak {p}
                 $}) is locally principal.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Moshe:2007:CMR,
  author =       "Yossi Moshe",
  title =        "On a Conjecture of {McIntosh} Regarding
                 {LP}-Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "599--610",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001139",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001139",
  abstract =     "A sequence over {\mathbb{Z}} is an LP-sequence if for
                 every prime p and integer n \geq 0 we have (mod p),
                 when is a base p expansion of n. In this paper, we
                 study sequences such that both, are LP-sequences for
                 some d \geq 2. One of those sequences is a
                 counter-example to a conjecture of McIntosh [15].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kraus:2007:CES,
  author =       "Alain Kraus",
  title =        "Courbes elliptiques semi-stables sur les corps de
                 nombres. ({French}) [{Semi}-stable elliptical curves on
                 number fields]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "611--633",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001127",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001127",
  abstract =     "Let K be a number field. In this paper, we are
                 interested in the following problem: does there exist a
                 constant c$_K$, which depends only on K, such that for
                 any semi-stable elliptic curve defined over K, the
                 Galois representation in its $p$-torsion points is
                 irreducible whenever p is a prime number greater than
                 c$_K$ ? In case the answer is positive, how can we get
                 such a constant? We prove that if a certain condition
                 is satisfied by K, the answer is positive and we obtain
                 c$_K$ explicitly. Furthermore, we prove that this
                 condition is realized in many situations.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Becheanu:2007:SCD,
  author =       "Mircea Becheanu and Florian Luca and Igor E.
                 Shparlinski",
  title =        "On the Sums of Complementary Divisors",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "635--648",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001152",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001152",
  abstract =     "In this paper, we study various arithmetic properties
                 of d + n/d, where d runs through all the \tau (n)
                 positive divisors of n. For example, denoting by \varpi
                 (n) the number of prime values among these sums, we
                 study how often \varpi (n) > 0 and also \varpi (n) =
                 \tau (n), and we also evaluate the average value of
                 \varpi (n). We estimate some character sums with d +
                 n/d and study the distribution of quadratic nonresidues
                 and primitive roots among these sums on average over n
                 \leq x.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Granville:2007:EPD,
  author =       "Andrew Granville",
  title =        "Erratum: {``Prime Divisors Are Poisson
                 Distributed''}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "649--651",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001073",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See \cite{Granville:2007:PDP}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001073",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2007:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 3)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "3",
  number =       "4",
  pages =        "653--654",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1142/S1793042107001164",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042107001164",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cooper:2008:CMF,
  author =       "Yaim Cooper and Nicholas Wage and Irena Wang",
  title =        "Congruences for Modular Forms of Non-Positive Weight",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "1--13",
  month =        feb,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042108001171",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001171",
  abstract =     "In this paper, we consider modular forms f(z) whose
                 $q$-series expansions \sum b(n)q$^n$ have coefficients
                 in a localized ring of algebraic integers. Extending
                 results of Serre and Ono, we show that if f has
                 non-positive weight, a congruence of the form b(\ell n
                 + a) \equiv 0 (mod \nu), where \nu is a place over \ell
                 in, can hold for only finitely many primes \ell \geq 5.
                 To obtain this, we establish an effective bound on \ell
                 in terms of the weight and the structure of f(z).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Takahashi:2008:APM,
  author =       "S. Takahashi",
  title =        "$p$-adic periods of modular elliptic curves and the
                 level-lowering theorem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "15--23",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001183",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001183",
  abstract =     "An elliptic curve defined over the field of rational
                 numbers can be considered as a complex torus. We can
                 describe its complex periods in terms of integration of
                 the weight-2 cusp form corresponding to the elliptic
                 curve. In this paper, we will study an analogous
                 description of the $p$-adic periods of the elliptic
                 curve, considering the elliptic curve as a $p$-adic
                 torus. An essential tool for the proof of such a
                 description is the level-lowering theorem of Ribet,
                 which is one of the main ingredients used in the proof
                 of Fermat's Last Theorem.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bundschuh:2008:ARC,
  author =       "Peter Bundschuh",
  title =        "Arithmetical results on certain $q$-series, {I}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "25--43",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001201",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001201",
  abstract =     "Entire transcendental solutions of certain mth order
                 linear q-difference equations with polynomial
                 coefficients are considered. The aim of this paper is
                 to give, under appropriate arithmetical conditions,
                 lower bounds for the dimension of the K-vector space
                 generated by 1 and the values of these solutions at m
                 successive powers of q, where K is the rational or an
                 imaginary quadratic number field. The main ingredients
                 of the proofs are, first, Nesterenko's dimension
                 estimate and its various generalizations, and secondly,
                 Popov's method (in T{\"o}pfer's version) for the
                 asymptotic evaluation of certain complex integrals.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Knafo:2008:ELB,
  author =       "Emmanuel Knafo",
  title =        "Effective Lower Bound for the Variance of Distribution
                 of Primes in Arithmetic Progressions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "45--56",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001213",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001213",
  abstract =     "Through a refinement for the estimation of the effect
                 of Siegel zeros, we show how to avoid the use of
                 Siegel's theorem in order to obtain the first {\em
                 effective\/} lower bound for the variance of
                 distribution of primes in arithmetic progressions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dujella:2008:PVP,
  author =       "Andrej Dujella and Clemens Fuchs and Florian Luca",
  title =        "A Polynomial Variant of a Problem of {Diophantus} for
                 Pure Powers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "57--71",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001225",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001225",
  abstract =     "In this paper, we prove that there does not exist a
                 set of 11 polynomials with coefficients in a field of
                 characteristic 0, not all constant, with the property
                 that the product of any two distinct elements plus 1 is
                 a perfect square. Moreover, we prove that there does
                 not exist a set of 5 polynomials with the property that
                 the product of any two distinct elements plus 1 is a
                 perfect kth power with k \geq 7. Combining these
                 results, we get an absolute upper bound for the size of
                 a set with the property that the product of any two
                 elements plus 1 is a pure power.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zhao:2008:WTT,
  author =       "Jianqiang Zhao",
  title =        "{Wolstenholme} Type Theorem for Multiple Harmonic
                 Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "73--106",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001146",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001146",
  abstract =     "In this paper, we will study the $p$-divisibility of
                 multiple harmonic sums (MHS) which are partial sums of
                 multiple zeta value series. In particular, we provide
                 some generalizations of the classical Wolstenholme's
                 Theorem to both homogeneous and non-homogeneous sums.
                 We make a few conjectures at the end of the paper and
                 provide some very convincing evidence.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rath:2008:DC,
  author =       "P. Rath and K. Srilakshmi and R. Thangadurai",
  title =        "On {Davenport}'s Constant",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "107--115",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001195",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001195",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kohl:2008:CCT,
  author =       "Stefan Kohl",
  title =        "On Conjugates of {Collatz}-Type Mappings",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "117--120",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001237",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001237",
  abstract =     "A mapping f : {\mathbb{Z}} \rightarrow {\mathbb{Z}} is
                 called {\em residue-class-wise affine\/} if there is a
                 positive integer m such that it is affine on residue
                 classes (mod m). If there is a finite set S \subset
                 {\mathbb{Z}} which intersects nontrivially with any
                 trajectory of f, then f is called {\em almost
                 contracting}. Assume that f is a surjective but not
                 injective residue-class-wise affine mapping, and that
                 the preimage of any integer under f is finite. Then f
                 is almost contracting if and only if there is a
                 permutation \sigma of {\mathbb{Z}} such that f$^{\sigma
                 }$ = \sigma$^{-1}$ \odot f \odot \sigma is
                 either monotonically increasing or monotonically
                 decreasing almost everywhere. In this paper it is shown
                 that if there is no positive integer k such that
                 applying f$^{(k)}$ decreases the absolute value of
                 almost all integers, then \sigma cannot be
                 residue-class-wise affine itself. The original
                 motivation for the investigations in this paper comes
                 from the famous 3n + 1 Conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Akbary:2008:SCP,
  author =       "Amir Akbary and Sean Alaric and Qiang Wang",
  title =        "On Some Classes of Permutation Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "121--133",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001249",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001249",
  abstract =     "Let p be a prime and q = p$^m$. We investigate
                 permutation properties of polynomials P(x) = x$^r$ +
                 x$^{r + s}$ + \cdots + x$^{r + ks}$ (0 < r < q - 1, 0 <
                 s < q - 1, and k \geq 0) over a finite field {$ \mathbb
                 {F} $}$_q$. More specifically, we construct several
                 classes of permutation polynomials of this form over {$
                 \mathbb {F} $}$_q$. We also count the number of
                 permutation polynomials in each class.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kirschenhofer:2008:FTT,
  author =       "P. Kirschenhofer and A. Peth{\H{o}} and J. M.
                 Thuswaldner",
  title =        "On a Family of Three Term Nonlinear Integer
                 Recurrences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "135--146",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001250",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001250",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Interlando:2008:FAG,
  author =       "J. Carmelo Interlando and Andr{\'e} Luiz Flores and
                 Trajano Pires {Da N{\'o}brega Neto}",
  title =        "A Family of Asymptotically Good Lattices Having a
                 Lattice in Each Dimension",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "1",
  pages =        "147--154",
  month =        feb,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001262",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:16 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001262",
  abstract =     "A new constructive family of asymptotically good
                 lattices with respect to sphere packing density is
                 presented. The family has a lattice in every dimension
                 n \geq 1. Each lattice is obtained from a conveniently
                 chosen integral ideal in a subfield of the cyclotomic
                 field {$ \mathbb {Q} $}(\zeta$_q$) where q is the
                 smallest prime congruent to 1 modulo n.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sun:2008:LTC,
  author =       "Zhi-Wei Sun and Daqing Wan",
  title =        "{Lucas}-type congruences for cyclotomic $ \psi
                 $-coefficients",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "155--170",
  month =        apr,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042108001286",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001286",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kazalicki:2008:LRC,
  author =       "Matija Kazalicki",
  title =        "Linear Relations for Coefficients of {Drinfeld}
                 Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "171--176",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001274",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001274",
  abstract =     "Choie, Kohnen and Ono have recently classified the
                 linear relations among the initial Fourier coefficients
                 of weight k modular forms on SL$_2$ ({\mathbb{Z}}), and
                 they employed these results to obtain particular
                 $p$-divisibility properties of some $p$-power Fourier
                 coefficients that are common to all modular forms of
                 certain weights. Using this, they reproduced some
                 famous results of Hida on non-ordinary primes. Here we
                 generalize these results to Drinfeld modular forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Abouzaid:2008:HLA,
  author =       "Mourad Abouzaid",
  title =        "Heights and logarithmic $ \gcd $ on algebraic curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "177--197",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001298",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001298",
  abstract =     "Let F(x,y) be an irreducible polynomial over {$
                 \mathbb {Q} $}, satisfying F(0,0) = 0. Skolem proved
                 that the integral solutions of F(x,y) = 0 with fixed
                 gcd are bounded [13] and Walsh gave an explicit bound
                 in terms of d = gcd(x,y) and F [16]. Assuming that
                 (0,0) is a non-singular point of the plane curve F(x,y)
                 = 0, we extend this result to algebraic solution, and
                 obtain an asymptotic equality instead of inequality. We
                 show that for any algebraic solution (\alpha , \beta),
                 the quotient h(\alpha)/log d is approximatively equal
                 to deg$_y$ F and the quotient h(\beta)/log d to deg$_x$
                 F; here h(\cdotp ) is the absolute logarithmic height
                 and d is the (properly defined) ``greatest common
                 divisor'' of \alpha and \beta.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mortenson:2008:BDP,
  author =       "Eric Mortenson",
  title =        "On the Broken $1$-Diamond Partition",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "199--218",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001365",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001365",
  abstract =     "We introduce a crank-like statistic for a different
                 class of partitions. In [4], Andrews and Paule
                 initiated the study of broken k-diamond partitions.
                 Their study of the respective generating functions led
                 to an infinite family of modular forms, about which
                 they were able to produce interesting arithmetic
                 theorems and conjectures for the related partition
                 functions. Here we establish a crank-like statistic for
                 the broken 1-diamond partition and discuss its role in
                 congruence properties.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alaca:2008:TFI,
  author =       "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Mathieu F.
                 Lemire and Kenneth S. Williams",
  title =        "Theta Function Identities and Representations by
                 Certain Quaternary Quadratic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "219--239",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001304",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001304",
  abstract =     "Some new theta function identities are proved and used
                 to determine the number of representations of a
                 positive integer n by certain quaternary quadratic
                 forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Harman:2008:WMV,
  author =       "Glyn Harman",
  title =        "{Watt}'s Mean Value Theorem and {Carmichael} Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "241--248",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001316",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001316",
  abstract =     "It is shown that Watt's new mean value theorem on sums
                 of character sums can be included in the method
                 described in the author's recent work [6] to show that
                 the number of Carmichael numbers up to x exceeds
                 x$^{{\u {2}153}}$ for all large x. This is done by
                 comparing the application of Watt's original version of
                 his mean value theorem [8] to the problem of primes in
                 short intervals [3] with the problem of finding
                 ``small'' primes in an arithmetic progression.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Watt:2008:BMV,
  author =       "Nigel Watt",
  title =        "Bounds for a Mean Value of Character Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "249--293",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001328",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001328",
  abstract =     "We obtain new upper bounds for the mean squared
                 modulus of sums $ \sum_{n \in \mathbb {N} } $ A$_n$
                 \chi (n), where the sequence (A$_n$) is fixed and the
                 variable \chi belongs to the set of non-principal
                 Dirichlet characters for some modulus q. It is assumed
                 that, for some M, some complex sequence (c$_m$)
                 satisfying $ c_m = 0$ for $ m \notin (M / 2, M]$, and
                 some $ \alpha (x)$ and $ \beta (y)$ (smooth functions
                 with compact support), one has $ A_n = \sum_{u v m = n}
                 \alpha (u) \beta (v) c_m (n \in \mathbb {N})$. There is
                 a natural analogy between the bounds obtained and
                 bounds on mean values of Dirichlet polynomials
                 previously obtained by Deshouillers and Iwaniec. Our
                 proofs make use of results from the spectral theory of
                 automorphic functions, including the bound of Kim and
                 Sarnak for the eigenvalues of Hecke operators acting on
                 certain spaces of Maass cusp forms. The results depend
                 on the size of $P$, the largest prime factor of $q$,
                 and improve as $ \log_q(P)$ is diminished. In separate
                 work, Harman has given an application of our results to
                 the theory of Carmichael numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Penniston:2008:ARP,
  author =       "David Penniston",
  title =        "Arithmetic of $ \ell $-regular partition functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "295--302",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001341",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001341",
  abstract =     "Let b$_{\ell }$ (n) denote the number of \ell -regular
                 partitions of n, where \ell is prime and 3 \leq \ell
                 \leq 23. In this paper we prove results on the
                 distribution of b$_{\ell }$ (n) modulo m for any odd
                 integer m > 1 with 3 \nmid m if \ell \neq 3.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bringmann:2008:RCO,
  author =       "Kathrin Bringmann and Jeremy Lovejoy",
  title =        "Rank and Congruences for Overpartition Pairs",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "303--322",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001353",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001353",
  abstract =     "The rank of an overpartition pair is a generalization
                 of Dyson's rank of a partition. The purpose of this
                 paper is to investigate the role that this statistic
                 plays in the congruence properties of, the number of
                 overpartition pairs of n. Some generating functions and
                 identities involving this rank are also presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Milas:2008:NTP,
  author =       "Antun Milas and Eric Mortenson and Ken Ono",
  title =        "Number Theoretic Properties of {Wronskians} of
                 {Andrews--Gordon} Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "2",
  pages =        "323--337",
  month =        apr,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001377",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001377",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nedev:2008:BSV,
  author =       "Zhivko Nedev and Anthony Quas",
  title =        "Balanced Sets and the Vector Game",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "339--347",
  month =        jun,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S179304210800133X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210800133X",
  abstract =     "We consider the notion of a balanced set modulo N. A
                 nonempty set S of residues modulo N is balanced if for
                 each x \in S, there is a d with 0 < d \leq N/2 such
                 that x \pm d mod N both lie in S. We define \alpha (N)
                 to be the minimum cardinality of a balanced set modulo
                 N. This notion arises in the context of a two-player
                 game that we introduce and has interesting connections
                 to the prime factorization of N. We demonstrate that
                 for p prime, \alpha (p) = \Theta (log p), giving an
                 explicit algorithmic upper bound and a lower bound
                 using finite field theory and show that for N
                 composite, \alpha (N) = min$_{p|N}$ \alpha (p).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Brueggeman:2008:LCD,
  author =       "Sharon Brueggeman and Darrin Doud",
  title =        "Local Corrections of Discriminant Bounds and Small
                 Degree Extensions of Quadratic Base Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "349--361",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001389",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001389",
  abstract =     "Using analytic techniques of Odlyzko and Poitou, we
                 create tables of lower bounds for discriminants of
                 number fields, including local corrections for ideals
                 of known norm. Comparing the lower bounds found in
                 these tables with upper bounds on discriminants of
                 number fields obtained from calculations involving
                 differents, we prove the nonexistence of a number of
                 small degree extensions of quadratic fields having
                 limited ramification. We note that several of our
                 results require the locally corrected bounds.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bacher:2008:NIH,
  author =       "Roland Bacher",
  title =        "A New Inequality for the {Hermite} Constants",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "363--386",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001390",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001390",
  abstract =     "We describe continuous increasing functions C$_n$ (x)
                 such that \gamma$_n$ \geq C$_n$ (\gamma$_{n - 1}$)
                 where \gamma$_m$ is Hermite's constant in dimension m.
                 This inequality yields a new proof of the
                 Minkowski--Hlawka bound \Delta$_n$ \geq \zeta (n)2$^{1
                 - n}$ for the maximal density \Delta$_n$ of
                 n-dimensional lattice packings.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Coulangeon:2008:EZF,
  author =       "Renaud Coulangeon",
  title =        "On {Epstein}'s Zeta Function of {Humbert} Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "387--401",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001407",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001407",
  abstract =     "The Epstein \zeta function \zeta (\Gamma, s) of a
                 lattice \Gamma is defined by a series which converges
                 for any complex number s such that {\mathfrak{R}} s >
                 n/2, and admits a meromorphic continuation to the
                 complex plane, with a simple pole at s = n/2. The
                 question as to which \Gamma, for a fixed s, minimizes
                 \zeta (\Gamma, s), has a long history, dating back to
                 Sobolev's work on numerical integration, and subsequent
                 papers by Delone and Ryshkov among others. This was
                 also investigated more recently by Sarnak and
                 Strombergsson. The present paper is concerned with
                 similar questions for positive definite quadratic forms
                 over number fields, also called {\em Humbert forms}.
                 We define Epstein zeta functions in that context and
                 study their meromorphic continuation and functional
                 equation, this being known in principle but somewhat
                 hard to find in the literature. Then, we give a general
                 criterion for a Humbert form to be {\em finally\/}
                 \zeta {\em extreme\/}, which we apply to a family of
                 examples in the last section.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Matsuno:2008:AII,
  author =       "Kazuo Matsuno",
  title =        "On the $2$-Adic {Iwasawa} Invariants of Ordinary
                 Elliptic Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "403--422",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001468",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001468",
  abstract =     "In this paper, we give an explicit formula describing
                 the variation of the 2-adic Iwasawa \lambda -invariants
                 attached to the Selmer groups of elliptic curves under
                 quadratic twists. To prove this formula, we extend some
                 results known for odd primes p, an analogue of Kida's
                 formula proved by Hachimori and the author and a
                 formula given by Greenberg and Vatsal, to the case
                 where p = 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lau:2008:LQN,
  author =       "Yuk-Kam Lau and Jie Wu",
  title =        "On the Least Quadratic Non-Residue",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "423--435",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001432",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001432",
  abstract =     "We prove that for almost all real primitive characters
                 \chi$_d$ of modulus |d|, the least positive integer
                 n$_{\chi d}$ at which \chi$_d$ takes a value not equal
                 to 0 and 1 satisfies n$_{\chi d}$ \ll log|d|, and give
                 a quite precise estimate on the size of the exceptional
                 set.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ong:2008:EET,
  author =       "Yao Lin Ong and Minking Eie and Wen-Chin Liaw",
  title =        "Explicit Evaluation of Triple {Euler} Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "437--451",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001420",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001420",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kochubei:2008:DCE,
  author =       "Anatoly N. Kochubei",
  title =        "{Dwork--Carlitz} Exponential and Overconvergence for
                 Additive Functions in Positive Characteristic",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "453--460",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001444",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001444",
  abstract =     "We study overconvergence phenomena for {$ \mathbb {F}
                 $}-linear functions on a function field over a finite
                 field {$ \mathbb {F} $}. In particular, an analog of
                 the Dwork exponential is introduced.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Toh:2008:GTO,
  author =       "Pee Choon Toh",
  title =        "Generalized $m$-th order {Jacobi} theta functions and
                 the {Macdonaldcg} identities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "461--474",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001456",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001456",
  abstract =     "We describe an mth order generalization of Jacobi's
                 theta functions and use these functions to construct
                 classes of theta function identities in multiple
                 variables. These identities are equivalent to the
                 Macdonald identities for the seven infinite families of
                 irreducible affine root systems. They are also
                 equivalent to some elliptic determinant evaluations
                 proven recently by Rosengren and Schlosser.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sankaranarayanan:2008:ESC,
  author =       "A. Sankaranarayanan and N. Saradha",
  title =        "Estimates for the Solutions of Certain {Diophantine}
                 Equations by {Runge}'s Method",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "475--493",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S179304210800147X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210800147X",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zhang:2008:ACS,
  author =       "Lingrui Zhang and Qin Yue",
  title =        "Another Case of a {Scholz}'s Theorem on Class Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "495--501",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001493",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001493",
  abstract =     "In this paper, we give necessary and sufficient
                 conditions for 8-ranks of narrow class groups of,
                 distinct primes p \equiv q \equiv 1 mod 4. The results
                 are useful for numerical computations.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Fukshansky:2008:SZQ,
  author =       "Lenny Fukshansky",
  title =        "Small Zeros of Quadratic Forms Over",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "3",
  pages =        "503--523",
  month =        jun,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001481",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001481",
  abstract =     "Let N \geq 2 be an integer, F a quadratic form in N
                 variables over, and an $L$-dimensional subspace, 1 \leq
                 L \leq N. We prove the existence of a small-height
                 maximal totally isotropic subspace of the bilinear
                 space (Z,F). This provides an analogue over of a
                 well-known theorem of Vaaler proved over number fields.
                 We use our result to prove an effective version of Witt
                 decomposition for a bilinear space over. We also
                 include some related effective results on orthogonal
                 decomposition and structure of isometries for a
                 bilinear space over. This extends previous results of
                 the author over number fields. All bounds on height are
                 explicit.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baruah:2008:SSS,
  author =       "Nayandeep Deka Baruah and Shaun Cooper and Michael
                 Hirschhorn",
  title =        "Sums of Squares and Sums of Triangular Numbers Induced
                 by Partitions of $8$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "525--538",
  month =        aug,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S179304210800150X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210800150X",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chapman:2008:AWT,
  author =       "Robin Chapman and Hao Pan",
  title =        "$q$-analogues of {Wilson}'s theorem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "539--547",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001511",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001511",
  abstract =     "We give q-analogues of Wilson's theorem for the primes
                 congruent to 1 and 3 modulo 4, respectively. Also
                 q-analogues of two congruences due to Mordell and
                 Chowla are established.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Schwab:2008:UFC,
  author =       "Emil Daniel Schwab and Pentti Haukkanen",
  title =        "A unique factorization in commutative {M{\"o}bius}
                 monoids",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "549--561",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001523",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001523",
  abstract =     "We show that any commutative M{\"o}bius monoid
                 satisfies a unique factorization theorem and thus
                 possesses arithmetical properties similar to those of
                 the multiplicative semigroup of positive integers.
                 Particular attention is paid to standard examples,
                 which arise from the bicyclic semigroup and the
                 multiplicative analogue of the bicyclic semigroup. The
                 second example shows that the Fundamental Theorem of
                 Arithmetic is a special case of the unique
                 factorization theorem in commutative M{\"o}bius
                 monoids. As an application, we study generalized
                 arithmetical functions defined on an arbitrary
                 commutative M{\"o}bius monoid.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Oura:2008:TSR,
  author =       "Manabu Oura and Cris Poor and David S. Yuen",
  title =        "Towards the {Siegel} Ring in Genus Four",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "563--586",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001535",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001535",
  abstract =     "Runge gave the ring of genus three Siegel modular
                 forms as a quotient ring, R$_3$ /{\u{3}008}J$^{(3)}$
                 {\u{3}009} where R$_3$ is the genus three ring of code
                 polynomials and J$^{(3)}$ is the difference of the
                 weight enumerators for the e$_8$ \oplus e$_8$ and
                 codes. Freitag and Oura gave a degree 24 relation,, of
                 the corresponding ideal in genus four; where is also a
                 linear combination of weight enumerators. We take
                 another step towards the ring of Siegel modular forms
                 in genus four. We explain new techniques for computing
                 with Siegel modular forms and actually compute six new
                 relations, classifying all relations through degree 32.
                 We show that the local codimension of any irreducible
                 component defined by these known relations is at least
                 3 and that the true ideal of relations in genus four is
                 not a complete intersection. Also, we explain how to
                 generate an infinite set of relations by symmetrizing
                 first order theta identities and give one example in
                 degree 32. We give the generating function of R$_5$ and
                 use it to reprove results of Nebe [25] and Salvati
                 Manni [37].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bonciocat:2008:CLP,
  author =       "Nicolae Ciprian Bonciocat",
  title =        "Congruences and {Lehmer}'s Problem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "587--596",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001547",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001547",
  abstract =     "We obtain explicit lower bounds for the Mahler measure
                 for nonreciprocal polynomials with integer coefficients
                 satisfying certain congruences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chakraborty:2008:ECG,
  author =       "Kalyan Chakraborty and Florian Luca and Anirban
                 Mukhopadhyay",
  title =        "Exponents of Class Groups of Real Quadratic Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "597--611",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001559",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001559",
  abstract =     "In this paper, we show that the number of real
                 quadratic fields {$ \mathbb {K} $} of discriminant $
                 \Delta_{ \mathbb {K}} < x $ whose class group has an
                 element of order $g$ (with $g$ even) is $ \geq x^{1 /
                 g} / 5 $ if $ x > x_0 $, uniformly for positive
                 integers $ g \leq (\log \log x) / (8 \log \log \log x)
                 $. We also apply the result to find real quadratic
                 number fields whose class numbers have many prime
                 factors.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Masri:2008:IFF,
  author =       "Nadia Masri",
  title =        "Infinite Families of Formulas for Sums of Integer
                 Squares",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "613--626",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001560",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001560",
  abstract =     "In 2002, Milne [5, 6] obtained ten infinite families
                 of formulas for the sums of integer squares. Recently,
                 Long and Yang [4] reproved four of these identities
                 using modular forms on various subgroups. In this
                 paper, we prove the remaining six, and show that all of
                 the identities can be proved by interpreting them in
                 terms of modular forms for \Gamma$_0$ (4).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Clark:2008:AHP,
  author =       "Pete L. Clark",
  title =        "An ``anti-{Hasse} Principle'' for Prime Twists",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "627--637",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001572",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001572",
  abstract =     "Given an algebraic curve $ C_{\mathbb {Q}} $ having
                 points everywhere locally and endowed with a suitable
                 involution, we show that there exists a positive
                 density family of prime quadratic twists of C violating
                 the Hasse principle. The result applies in particular
                 to $ w_N$-Atkin--Lehner twists of most modular curves
                 X$_0 (N)$ and to $ w_p$-Atkin--Lehner twists of certain
                 Shimura curves $ X^{D+}$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pineda-Ruelas:2008:EGG,
  author =       "Mario Pineda-Ruelas and Gabriel D. Villa-Salvador",
  title =        "Explicit {Galois} Group Realizations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "639--652",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001584",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001584",
  abstract =     "We study the embedding problem with abelian kernel and
                 we obtain a homogeneous system of equations, which
                 leads directly to the explicit realization of a finite
                 group with certain properties. We give an example
                 motivated by finding explicitly nonsolitary fields of
                 degree 18 over {$ \mathbb {Q} $}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Farag:2008:DTR,
  author =       "Hany M. Farag",
  title =        "{Dirichlet} Truncations of the {Riemann} Zeta Function
                 in the Critical Strip Possess Zeros Near Every Vertical
                 Line",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "653--662",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001596",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001596",
  abstract =     "We study the zeros of the finite truncations of the
                 alternating Dirichlet series expansion of the Riemann
                 zeta function in the critical strip. We do this with an
                 (admittedly highly) ambitious goal in mind. Namely,
                 that this series converges to the zeta function (up to
                 a trivial term) in the critical strip and our hope is
                 that if we can obtain good estimates for the zeros of
                 these approximations it may be possible to generalize
                 some of the results to zeta itself. This paper is a
                 first step towards this goal. Our results show that
                 these finite approximations have zeros near every
                 vertical line (so no vertical strip in this region is
                 zero-free). Furthermore, we give upper bounds for the
                 imaginary parts of the zeros (the real parts are
                 pinned). The bounds are numerically very large. Our
                 tools are: the inverse mapping theorem (for a
                 perturbative argument), the prime number theorem (for
                 counting primes), elementary geometry (for constructing
                 zeros of a related series), and a quantitative version
                 of Kronecker's theorem to go from one series to
                 another.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ash:2008:EUA,
  author =       "Avner Ash and David Pollack",
  title =        "Everywhere unramified automorphic cohomology for {$
                 \mathrm {SL}_3 (\mathbb {Z}) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "663--675",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001602",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001602",
  abstract =     "We conjecture that the only irreducible cuspidal
                 automorphic representations for GL$_3$ /{$ \mathbb
                 {Q}$} of cohomological type and level 1 are (up to
                 twisting) the symmetric square lifts of classical
                 cuspforms on GL$_2$ /{$ \mathbb {Q}$} of level 1. We
                 present computational evidence for this conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alaca:2008:BCF,
  author =       "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Kenneth S.
                 Williams",
  title =        "{Berndt}'s Curious Formula",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "677--689",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001614",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001614",
  abstract =     "A curious arithmetic formula deduced by Berndt from an
                 analytic formula of Ramanujan is proved arithmetically
                 and used to prove the formulae given by Liouville for
                 the number of representations of a positive integer by
                 the forms $ x^2 + y^2 + z^2 + t^2 + 2 u^2 + 2 v^2 $ and
                 $ x^2 + y^2 + 2 z^2 + 2 t^2 + 2 u^2 + 2 v^2 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Boca:2008:PES,
  author =       "Florin P. Boca",
  title =        "A problem of {Erd{\H{o}}s}, {Sz{\"o}sz} and
                 {Tur{\'a}n} concerning {Diophantine} approximations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "4",
  pages =        "691--708",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001626",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:17 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001626",
  abstract =     "For $ A > 0 $ and $ c > 1 $, let $ S(N, A, c) $ denote
                 the set of those numbers $ \theta \in ]0, 1 [ $ which
                 satisfy for some coprime integers $a$ and $b$ with $ N
                 < b \leq c N$. The problem of the existence and
                 computation of the limit $ f(A, c)$ of the Lebesgue
                 measure of $ S(N, A, c)$ as $ N \to \infty $ was raised
                 by Erd{\H{o}}s, Sz{\"u}sz and Tur{\'a}n [3]. This limit
                 has been shown to exist by Kesten and S{\'o}s [5] using
                 a probabilistic argument and explicitly computed when $
                 A c \leq 1$ by Kesten [4]. We give a complete solution
                 proving directly the existence of this limit and
                 identifying it in all cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chapman:2008:RIF,
  author =       "Robin Chapman",
  title =        "Representations of integers by the form $ x^2 + x y +
                 y^2 + z^2 + z t + t^2 $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "709--714",
  month =        oct,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042108001638",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001638",
  abstract =     "We give an elementary proof of the number of
                 representations of an integer by the quaternary
                 quadratic form x$^2$ + xy + y$^2$ + z$^2$ + zt +
                 t$^2$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Languasco:2008:HLP,
  author =       "Alessandro Languasco and Alessandro Zaccagnini",
  title =        "On the {Hardy--Littlewood} Problem in Short
                 Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "715--723",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S179304210800164X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210800164X",
  abstract =     "We study the distribution of Hardy--Littlewood numbers
                 in short intervals both unconditionally and
                 conditionally, i.e. assuming the Riemann Hypothesis
                 (RH). We prove that a suitable average of the
                 asymptotic formula for the number of representations of
                 a Hardy--Littlewood number holds in the interval [n, n
                 + H], where H < X$^{1 - 1 / k + \in }$ and n \in [X,
                 2X].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kopeliovich:2008:TCI,
  author =       "Yaacov Kopeliovich",
  title =        "Theta Constant Identities at Periods of Coverings of
                 Degree 3",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "725--733",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001663",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001663",
  abstract =     "We derive relations between theta functions evaluated
                 at period matrices of cyclic covers of order 3 ramified
                 above 3k points.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mizuno:2008:ALS,
  author =       "Yoshinori Mizuno",
  title =        "A $p$-adic limit of {Siegel--Eisenstein} series of
                 prime level $q$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "735--746",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001729",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001729",
  abstract =     "We show that a $p$-adic limit of a Siegel--Eisenstein
                 series of prime level q becomes a Siegel modular form
                 of level pq. This paper contains a simple formula for
                 Fourier coefficients of a Siegel--Eisenstein series of
                 degree two and prime levels.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ernvall-Hytonen:2008:ETA,
  author =       "Anne-Maria Ernvall-Hyt{\"o}nen",
  title =        "On the Error Term in the Approximate Functional
                 Equation for Exponential Sums Related to Cusp Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "747--756",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001730",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001730",
  abstract =     "We give a proof for the approximate functional
                 equation for exponential sums related to holomorphic
                 cusp forms and derive an upper bound for the error
                 term.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Thunder:2008:PBH,
  author =       "Jeffrey Lin Thunder",
  title =        "Points of Bounded Height on {Schubert} Varieties",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "757--765",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001742",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001742",
  abstract =     "Growth estimates and asymptotic estimates are given
                 for the number of rational points of bounded height on
                 Schubert varieties defined over number fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hassen:2008:HBP,
  author =       "Abdul Hassen and Hieu D. Nguyen",
  title =        "Hypergeometric {Bernoulli} Polynomials and {Appell}
                 Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "767--774",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001754",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001754",
  abstract =     "There are two analytic approaches to Bernoulli
                 polynomials B$_n$ (x): either by way of the generating
                 function ze$^{xz}$ /(e$^z$- 1) = \sum B$_n$ (x)z$^n$
                 /n! or as an Appell sequence with zero mean. In this
                 article, we discuss a generalization of Bernoulli
                 polynomials defined by the generating function z$^N$
                 e$^{xz}$ /(e$^z$- T$_{N - 1}$ (z)), where T$_N$ (z)
                 denotes the Nth Maclaurin polynomial of e$^z$, and
                 establish an equivalent definition in terms of Appell
                 sequences with zero moments in complete analogy to
                 their classical counterpart. The zero-moment condition
                 is further shown to generalize to Bernoulli polynomials
                 generated by the confluent hypergeometric series.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Onodera:2008:BSG,
  author =       "Kazuhiro Onodera",
  title =        "Behavior of Some Generalized Multiple Sine Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "775--796",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001651",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001651",
  abstract =     "Our aim is to investigate the behavior of generalized
                 multiple sine functions with general period parameters
                 in the fundamental domain. For that, we need to
                 calculate the number of their extremal values. By
                 estimating their special values, we determine it in
                 some cases including the quintuple sine function. As a
                 consequence, we sketch their graphs.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baoulina:2008:NSE,
  author =       "Ioulia Baoulina",
  title =        "On the number of solutions to the equation $ (x_1 +
                 \cdots + x_n)^2 = a x_1 \cdots x_n $ in a finite
                 field",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "797--817",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001675",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001675",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ford:2008:CFF,
  author =       "Kevin Ford and Igor Shparlinski",
  title =        "On Curves Over Finite Fields with {Jacobians} of Small
                 Exponent",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "819--826",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001687",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001687",
  abstract =     "We show that finite fields over which there is a curve
                 of a given genus g \geq 1 with its Jacobian having a
                 small exponent, are very rare. This extends a recent
                 result of Duke in the case of g = 1. We also show that
                 when g = 1 or g = 2, our lower bounds on the exponent,
                 valid for almost all finite fields {$ \mathbb {F}
                 $}$_q$ and all curves over {$ \mathbb {F} $}$_q$, are
                 best possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Leher:2008:BGN,
  author =       "Eli Leher",
  title =        "Bounds for the Genus of Numerical Semigroups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "827--834",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001699",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001699",
  abstract =     "We introduce a method to find upper and lower bounds
                 for the genus of numerical semigroups. Using it we
                 prove some old and new bounds for it and for the
                 Frobenius number of the semigroup.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jarden:2008:UFR,
  author =       "Moshe Jarden and Carlos R. Videla",
  title =        "Undecidability of Families of Rings of Totally Real
                 Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "835--850",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001705",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001705",
  abstract =     "Let {\mathbb{Z}}$_{tr}$ be the ring of totally real
                 integers, Gal({$ \mathbb {Q}$}) the absolute Galois
                 group of {$ \mathbb {Q}$}, and e a positive integer.
                 For each \sigma = (\sigma$_1$, \ldots, \sigma$_e$) \in
                 Gal({$ \mathbb {Q}$})$^e$ let {\mathbb{Z}}$_{tr}$
                 (\sigma) be the fixed ring in {\mathbb{Z}}$_{tr}$ of
                 \sigma$_1$, \ldots, \sigma$_e$. Then, the theory of all
                 first order sentences \theta that are true in
                 {\mathbb{Z}}$_{tr}$ (\sigma) for almost all \sigma \in
                 Gal({$ \mathbb {Q}$})$^e$ (in the sense of the Haar
                 measure) is undecidable.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zieve:2008:SFP,
  author =       "Michael E. Zieve",
  title =        "Some Families of Permutation Polynomials Over Finite
                 Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "851--857",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001717",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001717",
  abstract =     "We give necessary and sufficient conditions for a
                 polynomial of the form x$^r$ (1 + x$^v$ + x$^{2v}$ +
                 \cdots + x$^{kv}$ )$^t$ to permute the elements of the
                 finite field {$ \mathbb {F} $}$_q$. Our results yield
                 especially simple criteria in case (q - 1)/gcd(q - 1,
                 v) is a small prime.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Liu:2008:PIS,
  author =       "Yuancheng Liu",
  title =        "On the Problem of Integer Solutions to Decomposable
                 Form Inequalities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "5",
  pages =        "859--872",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001766",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001766",
  abstract =     "This paper proves a conjecture proposed by Chen and Ru
                 in [1] on the finiteness of the number of integer
                 solutions to decomposable form inequalities. Let k be a
                 number field and let F(X$_1$, \ldots, X$_m$) be a
                 non-degenerate decomposable form with coefficients in
                 k. We show that for every finite set of places S of k
                 containing the archimedean places of k, for each real
                 number \lambda < 1 and each constant c > 0, the
                 inequality has only finitely many -non-proportional
                 solutions, where H$_S$ (x$_1$, \ldots, x$_m$) =
                 \Pi$_{\upsilon \in S}$ max$_{1 \leq i \leq m}$ ||x$_i$
                 ||$_{\upsilon }$ is the S-height.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rosengren:2008:SSE,
  author =       "Hjalmar Rosengren",
  title =        "Sums of Squares from Elliptic {Pfaffians}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "873--902",
  month =        dec,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042108001778",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001778",
  abstract =     "We give a new proof of Milne's formulas for the number
                 of representations of an integer as a sum of 4m$^2$ and
                 4m(m + 1) squares. The proof is based on explicit
                 evaluation of pfaffians with elliptic function entries,
                 and relates Milne's formulas to Schur Q-polynomials and
                 to correlation functions for continuous dual Hahn
                 polynomials. We also state a new formula for 2m$^2$
                 squares.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Balasuriya:2008:CES,
  author =       "Sanka Balasuriya and William D. Banks and Igor E.
                 Shparlinski",
  title =        "Congruences and Exponential Sums with the Sum of
                 Aliquot Divisors Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "903--909",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S179304210800178X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210800178X",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kamano:2008:ABN,
  author =       "Ken Kamano",
  title =        "$p$-adic $q$-{Bernoulli} numbers and their
                 denominators",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "911--925",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S179304210800181X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210800181X",
  abstract =     "We define $p$-adic q-Bernoulli numbers by using a
                 $p$-adic integral. These numbers have good properties
                 similar to those of the classical Bernoulli numbers. In
                 particular, they satisfy an analogue of the von
                 Staudt--Clausen theorem, which includes information of
                 denominators of $p$-adic q-Bernoulli numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Balandraud:2008:IMN,
  author =       "{\'E}ric Balandraud",
  title =        "The Isoperimetric Method in Non-{Abelian} Groups with
                 an Application to Optimally Small Sumsets",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "927--958",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001821",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001821",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gurak:2008:PHK,
  author =       "S. Gurak",
  title =        "Polynomials for Hyper-{Kloosterman} Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "959--972",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001808",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001808",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Luca:2008:DE,
  author =       "Florian Luca and Alain Togb{\'e}",
  title =        "On the {Diophantine} equation $ x^2 + 2^a \cdot 5^b =
                 y^n $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "973--979",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001791",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001791",
  abstract =     "In this note, we find all the solutions of the
                 Diophantine equation x$^2$ + 2$^a$ \cdotp 5$^b$ = y$^n$
                 in positive integers x, y, a, b, n with x and y coprime
                 and n \geq 3.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Walling:2008:AHO,
  author =       "Lynne H. Walling",
  title =        "Action of {Hecke} Operators on {Siegel} Theta Series,
                 {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "981--1008",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001845",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001845",
  abstract =     "We apply the Hecke operators T(p)$^2$ and (1 \leq j
                 \leq n \leq 2k) to a degree n theta series attached to
                 a rank 2k {\mathbb{Z}}-lattice L equipped with a
                 positive definite quadratic form in the case that L/pL
                 is regular. We explicitly realize the image of the
                 theta series under these Hecke operators as a sum of
                 theta series attached to certain sublattices of,
                 thereby generalizing the Eichler Commutation Relation.
                 We then show that the average theta series (averaging
                 over isometry classes in a given genus) is an eigenform
                 for these operators. We explicitly compute the
                 eigenvalues on the average theta series, extending
                 previous work where we had the restrictions that \chi
                 (p) = 1 and n \leq k. We also show that for j > k when
                 \chi (p) = 1, and for j \geq k when \chi (p) = -1, and
                 that \theta (gen L) is an eigenform for T(p)$^2$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{El-Mahassni:2008:DCD,
  author =       "Edwin D. El-Mahassni and Domingo Gomez",
  title =        "On the Distribution of Counter-Dependent Nonlinear
                 Congruential Pseudorandom Number Generators in Residue
                 Rings",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "1009--1018",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001857",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001857",
  abstract =     "Nonlinear congruential pseudorandom number generators
                 can have unexpectedly short periods. Shamir and Tsaban
                 introduced the class of counter-dependent generators
                 which admit much longer periods. In this paper, using a
                 technique developed by Niederreiter and Shparlinski, we
                 present discrepancy bounds for sequences of s-tuples of
                 successive pseudorandom numbers generated by
                 counter-dependent generators modulo a composite M.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Khanduja:2008:TD,
  author =       "Sudesh K. Khanduja and Munish Kumar",
  title =        "On a Theorem of {Dedekind}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "1019--1025",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001833",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001833",
  abstract =     "Let K = {$ \mathbb {Q} $}(\theta) be an algebraic
                 number field with \theta in the ring A$_K$ of algebraic
                 integers of K and f(x) be the minimal polynomial of
                 \theta over the field {$ \mathbb {Q}$} of rational
                 numbers. For a rational prime p, let be the
                 factorization of the polynomial obtained by replacing
                 each coefficient of f(x) modulo p into product of
                 powers of distinct monic irreducible polynomials over
                 {\mathbb{Z}}/p{\mathbb{Z}}. Dedekind proved that if p
                 does not divide [A$_K$: {\mathbb{Z}}[\theta ]], then
                 the factorization of pA$_K$ as a product of powers of
                 distinct prime ideals is given by, with {$ \mathfrak
                 {p} $}$_i$ = pA$_K$ + g$_i$ (\theta)A$_K$, and residual
                 degree. In this paper, we prove that if the
                 factorization of a rational prime p in A$_K$ satisfies
                 the above-mentioned three properties, then p does not
                 divide [A$_K$ :{\mathbb{Z}}[\theta ]]. Indeed the
                 analogue of the converse is proved for general Dedekind
                 domains. The method of proof leads to a generalization
                 of one more result of Dedekind which characterizes all
                 rational primes p dividing the index of K.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Garthwaite:2008:CMT,
  author =       "Sharon Anne Garthwaite",
  title =        "The coefficients of the $ \omega (q) $ mock theta
                 function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "1027--1042",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001869",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001869",
  abstract =     "In 1920, Ramanujan wrote to Hardy about his discovery
                 of the mock theta functions. In the years since, there
                 has been much work in understanding the transformation
                 properties and asymptotic nature of these functions.
                 Recently, Zwegers proved a relationship between mock
                 theta functions and vector-valued modular forms, and
                 Bringmann and Ono used the theory of Maass forms and
                 Poincar{\'e} series to prove a conjecture of Andrews,
                 yielding an exact formula for the coefficients of the
                 f(q) mock theta function. Here we build upon these
                 results, using the theory of vector-valued modular
                 forms and Poincar{\'e} series to prove an exact formula
                 for the coefficients of the \omega (q) mock theta
                 function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{David:2008:PLA,
  author =       "Sinnou David and Am{\'i}lcar Pacheco",
  title =        "Le probl{\`e}me de {Lehmer} ab{\'e}lien pour un module
                 de {Drinfel'd}. ({French}) [{The} {Lehmer} abelien
                 problem for a {Drinfel'd} module]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "1043--1067",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001870",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001870",
  abstract =     "Let \varphi be a Drinfel'd module defined over a
                 finite extension K of {$ \mathbb {F} $}$_q$ (T); we
                 establish a uniform lower bound for the canonical
                 height of a point of \varphi, rational over the maximal
                 abelian extension of K, and thus solve the so-called
                 abelian version of the Lehmer problem in this
                 situation. The classical original problem (a non
                 torsion point in {$ \mathbb {G} $}$_m$ ({$ \mathbb
                 {Q}$}$^{ab}$)) was solved by Amoroso and Dvornicich
                 [1]. Soit \varphi un module de Drinfel'd d{\'e}fini sur
                 une extension finie K de {$ \mathbb {F} $}$_q$ (T);
                 nous d{\'e}montrons une minoration uniforme pour la
                 hauteur canonique d'un point de \varphi, rationnel sur
                 l'extension ab{\'e}lienne maximale de K, et
                 r{\'e}solvons ainsi la version dite ab{\'e}lienne du
                 probl{\`e}me de Lehmer dans cette situation. Dans le
                 cadre classique (un point d'ordre infini de {$ \mathbb
                 {G} $}$_m$ ({$ \mathbb {Q}$}$^{ab}$)), cette question a
                 {\'e}t{\'e} r{\'e}solue par Amoroso et Dvornicich dans
                 [1].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Anonymous:2008:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 4)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "4",
  number =       "6",
  pages =        "1069--1072",
  month =        dec,
  year =         "2008",
  DOI =          "https://doi.org/10.1142/S1793042108001900",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042108001900",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dewitt:2009:FGR,
  author =       "Meghan Dewitt and Darrin Doud",
  title =        "Finding {Galois} Representations Corresponding to
                 Certain {Hecke} Eigenclasses",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "1--11",
  month =        feb,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109001888",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001888",
  abstract =     "In 1992, Ash and McConnell presented computational
                 evidence of a connection between three-dimensional
                 Galois representations and certain arithmetic
                 cohomology classes. For some examples, they were unable
                 to determine the attached representation. For several
                 Hecke eigenclasses (including one for which Ash and
                 McConnell did not find the Galois representation), we
                 find a Galois representation which appears to be
                 attached and show strong evidence for the uniqueness of
                 this representation. The techniques that we use to find
                 defining polynomials for the Galois representations
                 include a targeted Hunter search, class field theory
                 and elliptic curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alaca:2009:NRP,
  author =       "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Mathieu F.
                 Lemire and Kenneth S. Williams",
  title =        "The Number of Representations of a Positive Integer by
                 Certain Quaternary Quadratic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "13--40",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001943",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001943",
  abstract =     "Some theta function identities are proved and used to
                 give formulae for the number of representations of a
                 positive integer by certain quaternary forms x$^2$ +
                 ey$^2$ + fz$^2$ + gt$^2$ with e, f, g \in {1, 2, 4,
                 8}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Singh:2009:DPS,
  author =       "Jitender Singh",
  title =        "Defining power sums of $n$ and $ \phi (n)$ integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "41--53",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900189X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900189X",
  abstract =     "Let n be a positive integer and \phi (n) denotes the
                 Euler phi function. It is well known that the power sum
                 of n can be evaluated in closed form in terms of n.
                 Also, the sum of all those \phi (n) positive integers
                 that are coprime to n and not exceeding n, is
                 expressible in terms of n and \phi (n). Although such
                 results already exist in literature, but here we have
                 presented some new analytical results in these
                 connections. Some functional and integral relations are
                 derived for the general power sums.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nathanson:2009:HFP,
  author =       "Melvyn B. Nathanson",
  title =        "Heights on the Finite Projective Line",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "55--65",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900192X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900192X",
  abstract =     "Define the height function h(a) = {mink + (ka mod p) :
                 k = 1, 2, \ldots, p - 1} for a \in {0, 1, \ldots, p -
                 1.} It is proved that the height has peaks at p, (p +
                 1)/2, and (p + c)/3, that these peaks occur at a =
                 [p/3], (p - 3)/2, (p - 1)/2, [2p/3], p - 3, p 2, and p
                 - 1, and that h(a) \leq p/3 for all other values of
                 a.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Azaiez:2009:RHM,
  author =       "Najib Ouled Azaiez",
  title =        "Restrictions of {Hilbert} Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "67--80",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001931",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001931",
  abstract =     "Let \Gamma \subset PSL(2, {\mathbb{R}}) be a discrete
                 and finite covolume subgroup. We suppose that the
                 modular curve is ``embedded'' in a Hilbert modular
                 surface, where \Gamma$_K$ is the Hilbert modular group
                 associated to a real quadratic field K. We define a
                 sequence of restrictions (\rho$_n$)$_{n \in \mathbb {N}
                 }$ of Hilbert modular forms for \Gamma$_K$ to modular
                 forms for \Gamma. We denote by M$_{k 1}$, k$_2$
                 (\Gamma$_K$) the space of Hilbert modular forms of
                 weight (k$_1$, k$_2$) for \Gamma$_K$. We prove that $
                 \sum_{n \in \mathbb {N} }$ $ \sum_{k 1}$, k$_2$ \in
                 \mathbb{N} \rho$_n$ (M$_{k 1}$, k$_2$ (\Gamma$_K$)) is
                 a subalgebra closed under Rankin--Cohen brackets of the
                 algebra \oplus$_{k \in \mathbb {N} }$ M$_k$ (\Gamma) of
                 modular forms for \Gamma.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Tanner:2009:SCP,
  author =       "Noam Tanner",
  title =        "Strings of Consecutive Primes in Function Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "81--88",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001918",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001918",
  abstract =     "In a recent paper, Thorne [5] proved the existence of
                 arbitrarily long strings of consecutive primes in
                 arithmetic progressions in the polynomial ring {$
                 \mathbb {F} $}$_q$ [t]. Here we extend this result to
                 show that given any k there exists a string of k
                 consecutive primes of degree D in arithmetic
                 progression for {\em all\/} sufficiently large D.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Wiese:2009:MSC,
  author =       "Gabor Wiese",
  title =        "On Modular Symbols and the Cohomology of {Hecke}
                 Triangle Surfaces",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "89--108",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001967",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001967",
  abstract =     "The aim of this article is to give a concise algebraic
                 treatment of the modular symbols formalism, generalized
                 from modular curves to Hecke triangle surfaces. A
                 sketch is included of how the modular symbols formalism
                 gives rise to the standard algorithms for the
                 computation of holomorphic modular forms. Precise and
                 explicit connections are established to the cohomology
                 of Hecke triangle surfaces and group cohomology. A
                 general commutative ring is used as coefficient ring in
                 view of applications to the computation of modular
                 forms over rings different from the complex numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Weston:2009:PRF,
  author =       "Tom Weston and Elena Zaurova",
  title =        "Power Residues of {Fourier} Coefficients of Elliptic
                 Curves with Complex Multiplication",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "109--124",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001955",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001955",
  abstract =     "Fix m greater than one and let E be an elliptic curve
                 over Q with complex multiplication. We formulate
                 conjectures on the density of primes p (congruent to
                 one modulo m) for which the pth Fourier coefficient of
                 E is an mth power modulo p; often these densities
                 differ from the naive expectation of 1/m. We also prove
                 our conjectures for m dividing the number of roots of
                 unity lying in the CM field of E; the most involved
                 case is m = 4 and complex multiplication by Q(i).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{AlHajjShehadeh:2009:GFH,
  author =       "Hala {Al Hajj Shehadeh} and Samar Jaafar and Kamal
                 Khuri-Makdisi",
  title =        "Generating Functions for {Hecke} Operators",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "125--140",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001979",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001979",
  abstract =     "Fix a prime N, and consider the action of the Hecke
                 operator T$_N$ on the space of modular forms of full
                 level and varying weight \kappa. The coefficients of
                 the matrix of T$_N$ with respect to the basis {E$_4^i$
                 E$_6^j$ | 4i + 6j = \kappa } for can be combined for
                 varying \kappa into a generating function F$_N$. We
                 show that this generating function is a rational
                 function for all N, and present a systematic method for
                 computing F$_N$. We carry out the computations for N =
                 2, 3, 5, and indicate and discuss generalizations to
                 spaces of modular forms of arbitrary level.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rhoades:2009:SPD,
  author =       "Robert C. Rhoades",
  title =        "Statistics of Prime Divisors in Function Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "141--152",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109001980",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001980",
  abstract =     "We show that the prime divisors of a random polynomial
                 in $ \mathbb {F}_q[t] $ are typically ``Poisson
                 distributed''. This result is analogous to the result
                 in {\mathbb{Z}} of Granville [1]. Along the way, we use
                 a sieve developed by Granville and Soundararajan [2] to
                 give a simple proof of the Erd{\H{o}}s--Kac theorem in
                 the function field setting. This approach gives
                 stronger results about the moments of the sequence $
                 \omega (f)_{f \in { \mathbb {F} } q} [t] $ than was
                 previously known, where $ \omega (f) $ is the number of
                 prime divisors of $f$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Raji:2009:FCG,
  author =       "Wissam Raji",
  title =        "{Fourier} Coefficients of Generalized Modular Forms of
                 Negative Weight",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "153--160",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002006",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002006",
  abstract =     "The Fourier coefficients of classical modular forms of
                 negative weights have been determined for the case for
                 which F(\tau) belongs to a subgroup of the full modular
                 group [9]. In this paper, we determine the Fourier
                 coefficients of generalized modular forms of negative
                 weights using the circle method.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Carr:2009:LIR,
  author =       "Richard Carr and Cormac O'Sullivan",
  title =        "On the Linear Independence of Roots",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "161--171",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002018",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002018",
  abstract =     "A set of real nth roots that is pairwise linearly
                 independent over the rationals must also be linearly
                 independent. We show how this result may be extended to
                 more general fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kuo:2009:GST,
  author =       "Wentang Kuo",
  title =        "A Generalization of the {Sato--Tate Conjecture}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "1",
  pages =        "173--184",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900202X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:18 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900202X",
  abstract =     "The original Sato--Tate Conjecture concerns the angle
                 distribution of the eigenvalues arisen from non-CM
                 elliptic curves. In this paper, we formulate an
                 analogue of the Sato--Tate Conjecture on automorphic
                 forms of (GL$_n$) and, under a holomorphic assumption,
                 prove that the distribution is either uniform or the
                 generalized Sato--Tate measure.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rivoal:2009:AAI,
  author =       "Tanguy Rivoal",
  title =        "Applications arithm{\'e}tiques de l'interpolation
                 lagrangienne. ({French}) [{Arithmetic} applications of
                 {Lagrangianp} interpolation]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "185--208",
  month =        mar,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109001992",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001992",
  abstract =     "Newton's polynomial interpolation was applied in many
                 situations in number theory, for example, to prove
                 Polya's famous theorem on the growth of arithmetic
                 entire function or the transcendency of e$^{\pi }$ by
                 Gel'fond. In this paper, we study certain arithmetic
                 applications of the rational interpolation defined by
                 Ren{\'e} Lagrange in 1935, which was never done before.
                 More precisely, we obtain new proofs of the
                 irrationality of the numbers log(2) and \zeta (3).
                 Furthermore, we provide a simultaneous generalization
                 of Newton and Lagrange's interpolations, which enables
                 us to get the irrationality of \zeta (2).
                 L'interpolation polynomiale de Newton a eu de tr{\`e}s
                 nombreuses applications arithm{\'e}tiques en
                 th{\'e}orie des nombres, comme le c{\'e}l{\`e}bre
                 th{\'e}or{\`e}me de Polya sur la croissance des
                 fonctions enti{\`e}res arithm{\'e}tiques ou encore la
                 transcendance de e$^{\pi }$ par Gel'fond. Dans ce
                 papier, on pr{\'e}sente certaines applications
                 arithm{\'e}tiques de l'interpolation rationnelle
                 d{\'e}finie par Ren{\'e} Lagrange en 1935, ce qui
                 n'avait jamais {\'e}t{\'e} fait auparavant. On retrouve
                 ainsi l'irrationalit{\'e} des nombres log(2) et \zeta
                 (3). On montre ensuite comment g{\'e}n{\'e}raliser
                 simultan{\'e}ment l'interpolation de Newton et celle de
                 Lagrange, ce qui nous permet de retrouver
                 l'irrationalit{\'e} de \zeta (2).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Chaumont:2009:CSL,
  author =       "Alain Chaumont and Johannes Leicht and Tom M{\"u}ller
                 and Andreas Reinhart",
  title =        "The Continuing Search for Large Elite Primes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "209--218",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002031",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002031",
  abstract =     "A prime number p is called {\em elite\/} if only
                 finitely many Fermat numbers 2$^{2 n}$ + 1 are
                 quadratic residues modulo p. So far, all 21 elite
                 primes less than 250 billion were known, together with
                 24 larger items. We completed the systematic search up
                 to the range of 2.5 \cdotp 10$^{12}$ finding six more
                 such numbers. Moreover, 42 new elites larger than this
                 bound were found, among which the largest has 374 596
                 decimal digits. A survey on the knowledge about elite
                 primes together with some open problems and conjectures
                 are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Yee:2009:BPT,
  author =       "Ae Ja Yee",
  title =        "Bijective Proofs of a Theorem of {Fine} and Related
                 Partition Identities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "219--228",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002043",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002043",
  abstract =     "In this paper, we prove a theorem of Fine bijectively.
                 Stacks with summits and gradual stacks with summits are
                 also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bandini:2009:CTE,
  author =       "A. Bandini and I. Longhi",
  title =        "Control Theorems for Elliptic Curves Over Function
                 Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "229--256",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002067",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002067",
  abstract =     "Let F be a global field of characteristic p > 0, {$
                 \mathbb {F} $}/F a Galois extension with and E/F a
                 non-isotrivial elliptic curve. We study the behavior of
                 Selmer groups Sel$_E$ (L)$_l$ (l any prime) as L varies
                 through the subextensions of {$ \mathbb {F} $} via
                 appropriate versions of Mazur's Control Theorem. In the
                 case l = p, we let {$ \mathbb {F} $} = \cup {$ \mathbb
                 {F} $}$_d$ where {$ \mathbb {F} $}$_d$ /F is a
                 -extension. We prove that Sel$_E$ ({$ \mathbb {F}
                 $}$_d$)$_p$ is a cofinitely generated {\mathbb{Z}}$_p$
                 [[Gal({\mathbb{Z}}$_d$ /F)]]-module and we associate to
                 its Pontrjagin dual a Fitting ideal. This allows to
                 define an algebraic {$L$}-function associated to E in
                 {\mathbb{Z}}$_p$ [[Gal({\mathbb{Z}}/F)]], providing an
                 ingredient for a function field analogue of Iwasawa's
                 Main Conjecture for elliptic curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Murty:2009:SVP,
  author =       "M. Ram Murty and N. Saradha",
  title =        "Special Values of the Polygamma Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "257--270",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002079",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002079",
  abstract =     "Let q be a natural number and. We consider the
                 Dirichlet series $ \sum_{n \geq 1} $ f(n)/n$^s$ and
                 relate its value when s is a natural number, to the
                 special values of the polygamma function. For certain
                 types of functions f, we evaluate the special value
                 explicitly and use this to study linear independence
                 over {$ \mathbb {Q}$} of L(k,\chi) as \chi ranges over
                 Dirichlet characters mod q which have the same parity
                 as k.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chida:2009:IOS,
  author =       "Masataka Chida",
  title =        "Indivisibility of Orders of {Selmer} Groups for
                 Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "271--280",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002080",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002080",
  abstract =     "In this paper, we consider indivisibility of orders of
                 Selmer groups for modular forms under quadratic twists.
                 Then, we will give a generalization of a theorem of
                 James--Ono and Kohnen--Ono.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kumchev:2009:BAE,
  author =       "Angel V. Kumchev",
  title =        "A Binary Additive Equation Involving Fractional
                 Powers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "281--292",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002092",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002092",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Li:2009:EPD,
  author =       "Xian-Jin Li",
  title =        "On the {Euler} Product of the {Dedekind} Zeta
                 Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "293--301",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002109",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002109",
  abstract =     "It is well known that the Euler product formula for
                 the Riemann zeta function \zeta (s) is still valid for
                 {\mathfrak{R}}(s) = 1 and s \neq 1. In this paper, we
                 extend this result to zeta functions of number fields.
                 In particular, we show that the Dedekind zeta function
                 \zeta$_k$ (s) for any algebraic number field k can be
                 written as the Euler product on the line
                 {\mathfrak{R}}(s) = 1 except at the point s = 1. As a
                 corollary, we obtain the Euler product formula on the
                 line {\mathfrak{R}}(s) = 1 for Dirichlet
                 {$L$}-functions L(s, \chi) of real characters.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Folsom:2009:CMU,
  author =       "Amanda Folsom",
  title =        "A Characterization of the Modular Units",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "303--310",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002110",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002110",
  abstract =     "We provide an exact formula for the complex exponents
                 in the modular product expansion of the modular units
                 in terms of the Kubert--Lang structure theory, and
                 deduce a characterization of the modular units in terms
                 of the growth of these exponents, answering a question
                 posed by Kohnen.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nitaj:2009:CRCo,
  author =       "Abderrahmane Nitaj",
  title =        "Cryptanalysis of {RSA} with Constrained Keys",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "311--325",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002122",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002122",
  abstract =     "Let n = pq be an RSA modulus with unknown prime
                 factors of equal bit-size. Let e be the public exponent
                 and d be the secret exponent satisfying ed \equiv 1 mod
                 \varphi (n) where \varphi (n) is the Euler totient
                 function. To reduce the decryption time or the
                 signature generation time, one might be tempted to use
                 a small private exponent d. Unfortunately, in 1990,
                 Wiener showed that private exponents smaller than are
                 insecure and in 1999, Boneh and Durfee improved the
                 bound to n$^{0.292}$. In this paper, we show that
                 instances of RSA with even large private exponents can
                 be efficiently broken if there exist positive integers
                 X, Y such that |eY - XF(u)| and Y are suitably small
                 where F is a function of publicly known expression for
                 which there exists an integer u \neq 0 satisfying F(u)
                 \approx n and pu or qu is computable from F(u) and n.
                 We show that the number of such exponents is at least
                 O(n$^{3 / 4 - \varepsilon }$) when F(u) = p(q - u).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Andrews:2009:SIA,
  author =       "George E. Andrews and Sylvie Corteel and Carla D.
                 Savage",
  title =        "On $q$-series identities arising from lecture hall
                 partitions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "327--337",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002134",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002134",
  abstract =     "In this paper, we highlight two $q$-series identities
                 arising from the ``five guidelines'' approach to
                 enumerating lecture hall partitions and give direct,
                 $q$-series proofs. This requires two new finite
                 corollaries of a q-analog of Gauss's second theorem. In
                 fact, the method reveals stronger results about lecture
                 hall partitions and anti-lecture hall compositions that
                 are only partially explained combinatorially.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pila:2009:EFS,
  author =       "Jonathan Pila",
  title =        "Entire Functions Sharing Arguments of Integrality,
                 {I}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "339--353",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002146",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002146",
  abstract =     "Let f be an entire function that is real and strictly
                 increasing for all sufficiently large real arguments,
                 and that satisfies certain additional conditions, and
                 let X$_f$ be the set of non-negative real numbers at
                 which f is integer valued. Suppose g is an entire
                 function that takes integer values on X$_f$. We find
                 growth conditions under which f,g must be algebraically
                 dependent (over {\mathbb{Z}}) on X. The result
                 generalizes a weak form of a theorem of P{\'o}lya.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Tanigawa:2009:FPM,
  author =       "Yoshio Tanigawa and Wenguang Zhai",
  title =        "On the fourth power moment of {$ \Delta x $} and {$
                 E(x) $} in short intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "2",
  pages =        "355--382",
  month =        mar,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002055",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002055",
  abstract =     "Let \Delta (x) and E(x) be error terms of the sum of
                 divisor function and the mean square of the Riemann
                 zeta function, respectively. In this paper, their
                 fourth power moments for short intervals of Jutila's
                 type are considered. We get an asymptotic formula for U
                 in some range.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sands:2009:VFM,
  author =       "Jonathan W. Sands",
  title =        "Values at $ s = - 1 $ of {$L$}-functions for
                 multi-quadratic extensions of number fields, and the
                 fitting ideal of the tame kernel",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "383--405",
  month =        may,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109002183",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002183",
  abstract =     "Fix a Galois extension of totally real number fields
                 such that the Galois group G has exponent 2. Let S be a
                 finite set of primes of F containing the infinite
                 primes and all those which ramify in, let denote the
                 primes of lying above those in S, and let denote the
                 ring of -integers of. We then compare the Fitting ideal
                 of as a {\mathbb{Z}}[G]-module with a higher
                 Stickelberger ideal. The two extend to the same ideal
                 in the maximal order of {$ \mathbb {Q} $}[G], and hence
                 in {\mathbb{Z}}[1/2][G]. Results in {\mathbb{Z}}[G] are
                 obtained under the assumption of the Birch--Tate
                 conjecture, especially for biquadratic extensions,
                 where we compute the index of the higher Stickelberger
                 ideal. We find a sufficient condition for the Fitting
                 ideal to contain the higher Stickelberger ideal in the
                 case where is a biquadratic extension of F containing
                 the first layer of the cyclotomic
                 {\mathbb{Z}}$_2$-extension of F, and describe a class
                 of biquadratic extensions of F = {$ \mathbb {Q}$} that
                 satisfy this condition.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baccar:2009:SSP,
  author =       "N. Baccar and F. {Ben Sa{\"i}d}",
  title =        "On Sets Such That the Partition Function Is Even from
                 a Certain Point On",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "407--428",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002195",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002195",
  abstract =     "Let P \in {$ \mathbb {F} $}$_2$ [z] with P(0) = 1 and
                 degree(P) \geq 1. It is not difficult to prove (cf.
                 [4,14]) that there is a unique subset of \mathbb{N}
                 such that (mod 2), where denotes the number of
                 partitions of n with parts in. However, finding the
                 elements of such sets for general P seems to be hard.
                 In this paper, we obtain solutions to this problem for
                 a large class of polynomials P. Moreover, we give
                 asymptotics for the counting function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chu:2009:ISH,
  author =       "Wenchang Chu and Deyin Zheng",
  title =        "Infinite Series with Harmonic Numbers and Central
                 Binomial Coefficients",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "429--448",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002171",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002171",
  abstract =     "By means of two hypergeometric summation formulae, we
                 establish two large classes of infinite series
                 identities with harmonic numbers and central binomial
                 coefficients. Up to now, these numerous formulae have
                 hidden behind very few known identities of
                 Ap{\'e}ry-like series for Riemann-zeta function,
                 discovered mainly by Lehmer [14] and Elsner [12] as
                 well as Borwein {\em et al.\/} [4, 5, 7]. All the
                 computation and verification are carried out by an
                 appropriately-devised {\em Mathematica\/} package.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ding:2009:SIF,
  author =       "Shanshan Ding",
  title =        "Smallest irreducible of the form $ x^2 - d y^2 $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "449--456",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002158",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002158",
  abstract =     "It is a classical result that prime numbers of the
                 form x$^2$ + ny$^2$ can be characterized via class
                 field theory for an infinite set of n. In this paper,
                 we derive the function field analogue of the classical
                 result. Then, we apply an effective version of the
                 Chebotarev density theorem to bound the degree of the
                 smallest irreducible of the form x$^2$- dy$^2$, where
                 x, y, and d are elements of a polynomial ring over a
                 finite field.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kominers:2009:CEE,
  author =       "Scott Duke Kominers",
  title =        "Configurations of Extremal Even Unimodular Lattices",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "457--464",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900216X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900216X",
  abstract =     "We extend the results of Ozeki on the configurations
                 of extremal even unimodular lattices. Specifically, we
                 show that if L is such a lattice of rank 56, 72, or 96,
                 then L is generated by its minimal-norm vectors.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Akbary:2009:RSM,
  author =       "Amir Akbary and V. Kumar Murty",
  title =        "Reduction $ \bmod p $ of subgroups of the
                 {Mordell--Weil} group of an elliptic curve",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "465--487",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002225",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002225",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kurlberg:2009:PSS,
  author =       "P{\"a}r Kurlberg",
  title =        "{Poisson} Spacing Statistics for Value Sets of
                 Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "489--513",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002237",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002237",
  abstract =     "If f is a non-constant polynomial with integer
                 coefficients and q is an integer, we may regard f as a
                 map from Z/qZ to Z/qZ. We show that the distribution of
                 the (normalized) spacings between consecutive elements
                 in the image of these maps becomes {\em Poissonian\/}
                 as q tends to infinity along any sequence of square
                 free integers such that the mean spacing modulo q tends
                 to infinity.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Shavgulidze:2009:NRI,
  author =       "Ketevan Shavgulidze",
  title =        "On the Number of Representations of Integers by the
                 Sums of Quadratic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "515--525",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002201",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002201",
  abstract =     "We shall obtain the formulae for the number of
                 representations of positive integers by a direct sum of
                 k binary quadratic forms of the kind, when k = 3, 4,
                 5.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bosca:2009:PIA,
  author =       "S{\'e}bastien Bosca",
  title =        "Principalization of Ideals in {Abelian} Extensions of
                 Number Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "527--539",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002213",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002213",
  abstract =     "We give a self-contained proof of a general conjecture
                 of Gras on principalization of ideals in Abelian
                 extensions of a given field L, which was solved by
                 Kurihara in the case of totally real extensions L of
                 the rational field {$ \mathbb {Q} $}. More precisely,
                 for any given extension L/K of number fields, in which
                 at least one infinite place of K totally splits, and
                 for any ideal class c$_L$ of L, we construct a finite
                 Abelian extension F/K, in which all infinite places
                 totally split, such that c$_L$ become principal in the
                 compositum M = LF.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sapar:2009:MEA,
  author =       "S. H. Sapar and K. A. Mohd. Atan",
  title =        "A method of estimating the $p$-adic sizes of common
                 zeros of partial derivative polynomials associated with
                 a quintic form",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "3",
  pages =        "541--554",
  month =        may,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002249",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:19 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002249",
  abstract =     "It is known that the value of the exponential sum can
                 be derived from the estimate of the cardinality |V|,
                 the number of elements contained in the set where is
                 the partial derivatives of with respect to. The
                 cardinality of V in turn can be derived from the
                 $p$-adic sizes of common zeros of the partial
                 derivatives. This paper presents a method of
                 determining the $p$-adic sizes of the components of
                 (\xi, \eta) a common root of partial derivative
                 polynomials of f(x,y) in $ Z_p$ [x,y] of degree five
                 based on the $p$-adic Newton polyhedron technique
                 associated with the polynomial. The degree five
                 polynomial is of the form f(x,y) = ax$^5$ + bx$^4$ y +
                 cx$^3$ y$^2$ + sx + ty + k. The estimate obtained is in
                 terms of the $p$-adic sizes of the coefficients of the
                 dominant terms in f.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kida:2009:QPH,
  author =       "Masanari Kida and Gu{\'e}na{\"e}l Renault and Kazuhiro
                 Yokoyama",
  title =        "Quintic Polynomials of {Hashimoto--Tsunogai}, {Brumer}
                 and {Kummer}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "555--571",
  month =        jun,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109002250",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002250",
  abstract =     "We establish an isomorphism between the quintic cyclic
                 polynomials discovered by Hashimoto--Tsunogai and those
                 arising from Kummer theory for certain algebraic tori.
                 This enables us to solve the isomorphism problem for
                 Hashimoto--Tsunogai polynomials and also Brumer's
                 quintic polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bringmann:2009:CDR,
  author =       "Kathrin Bringmann",
  title =        "Congruences for {Dyson}'s Ranks",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "573--584",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002262",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002262",
  abstract =     "In this paper, we prove infinite families of
                 congruences for coefficients of harmonic Maass forms
                 whose coefficients encode Dyson's rank. This
                 generalizes the earlier joint work of the author with
                 Ken Ono.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alvanos:2009:CAC,
  author =       "Paraskevas Alvanos and Yuri Bilu and Dimitrios
                 Poulakis",
  title =        "Characterizing Algebraic Curves with Infinitely Many
                 Integral Points",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "585--590",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002274",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002274",
  abstract =     "A classical theorem of Siegel asserts that the set of
                 S-integral points of an algebraic curveC over a number
                 field is finite unless C has genus 0 and at most two
                 points at infinity. In this paper, we give necessary
                 and sufficient conditions for C to have infinitely many
                 S-integral points.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kozuma:2009:ECR,
  author =       "Rintaro Kozuma",
  title =        "Elliptic Curves Related to Cyclic Cubic Extensions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "591--623",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002304",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002304",
  abstract =     "The aim of this paper is to study certain family of
                 elliptic curves defined over a number field F arising
                 from hyperplane sections of some cubic surface
                 associated to a cyclic cubic extension K/F. We show
                 that each admits a 3-isogeny \varphi over F and the
                 dual Selmer group is bounded by a kind of unit/class
                 groups attached to K/F. This is proven via certain
                 rational function on the elliptic curve with nice
                 property. We also prove that the Shafarevich--Tate
                 group coincides with a class group of K as a special
                 case.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Konyagin:2009:SPC,
  author =       "Sergei V. Konyagin and Melvyn B. Nathanson",
  title =        "Sums of Products of Congruence Classes and of
                 Arithmetic Progressions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "625--634",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002286",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002286",
  abstract =     "Consider the congruence class R$_m$ (a) = {a + im : i
                 \in Z} and the infinite arithmetic progression P$_m$
                 (a) = {a + im : i \in N$_0$ }. For positive integers
                 a,b,c,d,m the sum of products set R$_m$ (a)R$_m$ (b) +
                 R$_m$ (c)R$_m$ (d) consists of all integers of the form
                 (a+im) \cdotp (b+jm)+(c+km)(d+\ell m) for some
                 i,j,k,\ell \in Z. It is proved that if gcd(a,b,c,d,m) =
                 1, then R$_m$ (a)R$_m$ (b) + R$_m$ (c)R$_m$ (d) is
                 equal to the congruence class R$_m$ (ab+cd), and that
                 the sum of products set P$_m$ (a)P$_m$ (b)+P$_m$
                 (c)P$_m$ eventually coincides with the infinite
                 arithmetic progression P$_m$ (ab+cd).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Oura:2009:EPA,
  author =       "Manabu Oura",
  title =        "{Eisenstein} Polynomials Associated to Binary Codes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "635--640",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002298",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002298",
  abstract =     "The Eisenstein polynomial is the weighted sum of the
                 weight enumerators of all classes of Type II codes of
                 fixed length. In this note, we investigate the ring
                 generated by Eisenstein polynomials in genus 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Moree:2009:PPA,
  author =       "P. Moree and B. Sury",
  title =        "Primes in a Prescribed Arithmetic Progression Dividing
                 the Sequence",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "641--665",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002316",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002316",
  abstract =     "Given positive integers a,b,c and d such that c and d
                 are coprime, we show that the primes p \equiv c (mod d)
                 dividing a$^k$ +b$^k$ for some k \geq 1 have a natural
                 density and explicitly compute this density. We
                 demonstrate our results by considering some claims of
                 Fermat that he made in a 1641 letter to Mersenne.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Tretkoff:2009:TSV,
  author =       "Marvin D. Tretkoff and Paula Tretkoff",
  title =        "Transcendence of Special Values of {Pochhammer}
                 Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "667--677",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900233X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900233X",
  abstract =     "In this paper, we examine the set of algebraic numbers
                 at which higher order hypergeometric functions take
                 algebraic values. In particular, we deduce criteria for
                 this set to be finite and for it to be infinite.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vulakh:2009:MSC,
  author =       "L. Ya. Vulakh",
  title =        "The {Markov} Spectra for Cocompact {Fuchsian} Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "679--718",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002341",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002341",
  abstract =     "Applying the Klein model D$^2$ of the hyperbolic plane
                 and identifying the geodesics in D$^2$ with their poles
                 in the projective plane, the author has developed a
                 method for finding the discrete part of the Markov
                 spectrum for Fuchsian groups. It is applicable mostly
                 to non-cocompact groups. In the present paper, this
                 method is extended to cocompact Fuchsian groups. For a
                 group with signature (0;2,2,2,3), the complete
                 description of the discrete part of the Markov spectrum
                 is obtained. The result obtained leads to the complete
                 description of the Markov and Lagrange spectra for the
                 imaginary quadratic field with discriminant -20.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hofer:2009:DPG,
  author =       "Roswitha Hofer and Peter Kritzer and Gerhard Larcher
                 and Friedrich Pillichshammer",
  title =        "Distribution properties of generalized {Van Der
                 Corput--Halton} sequences and their subsequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "4",
  pages =        "719--746",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002328",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002328",
  abstract =     "We study the distribution properties of sequences
                 which are a generalization of the well-known van der
                 Corput--Halton sequences on one hand, and digital
                 (T,s)-sequences on the other. In this paper, we give
                 precise results concerning the distribution properties
                 of such sequences in the s-dimensional unit cube.
                 Moreover, we consider subsequences of the
                 above-mentioned sequences and study their distribution
                 properties. Additionally, we give discrepancy estimates
                 for some special cases, including subsequences of van
                 der Corput and van der Corput--Halton sequences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Adolphson:2009:ESI,
  author =       "Alan Adolphson and Steven Sperber",
  title =        "Exponential sums on {$ \mathbb {A}^n $}. {IV}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "747--764",
  month =        aug,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109002353",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002353",
  abstract =     "We find new conditions on a polynomial over a finite
                 field that guarantee that the exponential sum defined
                 by the polynomial has only one nonvanishing $p$-adic
                 cohomology group, hence the {$L$}-function associated
                 to the exponential sum is a polynomial or the
                 reciprocal of a polynomial.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cooper:2009:CES,
  author =       "Shaun Cooper",
  title =        "Construction of {Eisenstein} series for {$ \Gamma_0
                 (p) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "765--778",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002365",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002365",
  abstract =     "A simple construction of Eisenstein series for the
                 congruence subgroup \Gamma$_0$ (p) is given. The
                 construction makes use of the Jacobi triple product
                 identity and Gauss sums, but does not use the modular
                 transformation for the Dedekind eta-function. All
                 positive integral weights are handled in the same way,
                 and the conditionally convergent cases of weights 1 and
                 2 present no extra difficulty.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Salle:2009:MPG,
  author =       "Landry Salle",
  title =        "Mild pro-$p$-groups as {Galois} groups over global
                 fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "779--795",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002377",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002377",
  abstract =     "This paper is devoted to finding new examples of mild
                 pro-p-groups as Galois groups over global fields,
                 following the work of Labute ([6]). We focus on the
                 Galois group of the maximal T-split S-ramified
                 pro-p-extension of a global field k. We first retrieve
                 some facts on presentations of such a group, including
                 a study of the local-global principle for the
                 cohomology group, then we show separately in the case
                 of function fields and in the case of number fields how
                 it can be used to find some mild pro-p-groups.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Byard:2009:TPQ,
  author =       "Kevin Byard",
  title =        "Tenth Power Qualified Residue Difference Sets",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "797--803",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002389",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002389",
  abstract =     "Qualified residue difference sets of power n are known
                 to exist for n = 2, 4, 6, as do similar sets that
                 include the zero element, while both classes of set are
                 known to be nonexistent for n = 8. Both classes of set
                 are proved nonexistent for n = 10.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Taylor:2009:ACN,
  author =       "Karen Taylor",
  title =        "Analytic Continuation of Nonanalytic Vector-Valued
                 {Eisenstein} Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "805--830",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002407",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002407",
  abstract =     "In this paper, we introduce a vector-valued
                 nonanalytic Eisenstein series appearing naturally in
                 the Rankin--Selberg convolution of a vector-valued
                 modular cusp form associated to a monomial
                 representation \rho of SL(2,{\mathbb{Z}}). This
                 vector-valued Eisenstein series transforms under a
                 representation \chi$_{\rho }$ associated to \rho. We
                 use a method of Selberg to obtain an analytic
                 continuation of this vector-valued nonanalytic
                 Eisenstein series to the whole complex plane.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jaafar:2009:M,
  author =       "Samar Jaafar and Kamal Khuri-Makdisi",
  title =        "On the maps from {$ X(4 p) $} to {$ X(4) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "831--844",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002390",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002390",
  abstract =     "We study pullbacks of modular forms of weight 1 from
                 the modular curve X(4) to the modular curve X(4p),
                 where p is an odd prime. We find the extent to which
                 such modular forms separate points on X(4p). Our main
                 result is that these modular forms give rise to a
                 morphism F from the quotient of X(4p) by a certain
                 involution \iota to projective space, such that F is a
                 projective embedding of X(4p)/\iota away from the
                 cusps. We also report on computer calculations
                 regarding products of such modular forms, going up to
                 weight 4 for p \leq 13, and up to weight 3 for p \leq
                 23, and make a conjecture about these products and the
                 nature of the singularities at the cusps of the image
                 F(X(4p)/\iota).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Knopp:2009:PGM,
  author =       "Marvin Knopp and Geoffrey Mason",
  title =        "Parabolic Generalized Modular Forms and Their
                 Characters",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "845--857",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002419",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See revisions \cite{Knopp:2012:RPG}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002419",
  abstract =     "We make a detailed study of the {\em generalized
                 modular forms\/} of weight zero and their associated
                 multiplier systems (characters) on an arbitrary
                 subgroup \Gamma of finite index in the modular group.
                 Among other things, we show that every generalized
                 divisor on the compact Riemann surface associated to
                 \Gamma is the divisor of a modular form (with {\em
                 unitary\/} character) which is unique up to scalars.
                 This extends a result of Petersson, and has
                 applications to the Eichler cohomology.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Suarez:2009:MLC,
  author =       "Ivan Suarez",
  title =        "Modular Lattices Over {CM} Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "859--869",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002420",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002420",
  abstract =     "We study some properties of Arakelov-modular lattices,
                 which are particular modular ideal lattices over CM
                 fields. There are two main results in this paper. The
                 first one is the determination of the number of
                 Arakelov-modular lattices of fixed level over a given
                 CM field provided that an Arakelov-modular lattice is
                 already known. This number depends on the class numbers
                 of the CM field and its maximal totally real subfield.
                 The first part gives also a way to compute all these
                 Arakelov-modular lattices. In the second part, we
                 describe the levels that can occur for some
                 multiquadratic CM number fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  keywords =     "CM (complex multiplication)",
}

@Article{Angles:2009:WNC,
  author =       "Bruno Angl{\`e}s and Tatiana Beliaeva",
  title =        "On {Weil} Numbers in Cyclotomic Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "871--884",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002432",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002432",
  abstract =     "In this paper, we study the $p$-adic behavior of Weil
                 numbers in the cyclotomic {\mathbb{Z}}$_p$-extension of
                 the pth cyclotomic field. We determine the
                 characteristic ideal of the quotient of semi-local
                 units by Weil numbers in terms of the characteristic
                 ideals of some classical modules that appear in the
                 Iwasawa theory. In a recent preprint [9] by Nguyen
                 Quang Do and Nicolas, a generalization of this result
                 to a semi-simple case was obtained.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dobi:2009:SRT,
  author =       "Doris Dobi and Nicholas Wage and Irena Wang",
  title =        "Supersingular Rank Two {Drinfel'd} Modules and Analogs
                 of {Atkin}'s Orthogonal Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "885--895",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002444",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002444",
  abstract =     "The theory of elliptic curves and modular forms
                 provides a precise relationship between the
                 supersingular j-invariants and the congruences between
                 modular forms. Kaneko and Zagier discuss a surprising
                 generalization of these results in their paper on Atkin
                 orthogonal polynomials. In this paper, we define an
                 analog of the Atkin orthogonal polynomials for rank two
                 Drinfel'd modules.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Glass:2009:RHC,
  author =       "Darren Glass",
  title =        "The $2$-Ranks of Hyperelliptic Curves with Extra
                 Automorphisms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "897--910",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002468",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002468",
  abstract =     "This paper examines the relationship between the
                 automorphism group of a hyperelliptic curve defined
                 over an algebraically closed field of characteristic
                 two and the 2-rank of the curve. In particular, we
                 exploit the wild ramification to use the
                 Deuring--Shafarevich formula in order to analyze the
                 ramification of hyperelliptic curves that admit extra
                 automorphisms and use this data to impose restrictions
                 on the genera and 2-ranks of such curves. We also show
                 how some of the techniques and results carry over to
                 the case where our base field is of characteristic p >
                 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Delaunay:2009:SPE,
  author =       "Christophe Delaunay and Christian Wuthrich",
  title =        "Self-Points on Elliptic Curves of Prime Conductor",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "5",
  pages =        "911--932",
  month =        aug,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002456",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002456",
  abstract =     "Let E be an elliptic curve of conductor p. Given a
                 cyclic subgroup C of order p in E[p], we construct a
                 modular point P$_C$ on E, called self-point, as the
                 image of (E,C) on X$_0$ (p) under the modular
                 parametrization X$_0$ (p) \rightarrow E. We prove that
                 the point is of infinite order in the Mordell--Weil
                 group of E over the field of definition of C. One can
                 deduce a lower bound on the growth of the rank of the
                 Mordell--Weil group in its PGL$_2$
                 ({\mathbb{Z}}$_p$)-tower inside {$ \mathbb
                 {Q}$}(E[p$^{\infty }$ ]).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Languasco:2009:CRE,
  author =       "Alessandro Languasco",
  title =        "A Conditional Result on the Exceptional Set for
                 {Hardy--Littlewood} Numbers in Short Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "933--951",
  month =        sep,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S179304210900247X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900247X",
  abstract =     "Assuming the Generalized Riemann Hypothesis holds, we
                 prove some conditional estimates on the exceptional set
                 in short intervals for the Hardy--Littlewood problem.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bajnok:2009:MSS,
  author =       "B{\'e}la Bajnok",
  title =        "On the maximum size of a $ (k, l)$-sum-free subset of
                 an abelian group",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "953--971",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002481",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002481",
  abstract =     "A subset A of a given finite abelian group G is called
                 (k,l)-sum-free if the sum of k (not necessarily
                 distinct) elements of A does not equal the sum of l
                 (not necessarily distinct) elements of A. We are
                 interested in finding the maximum size \lambda$_{k, l}$
                 (G) of a (k,l)-sum-free subset in G. A (2,1)-sum-free
                 set is simply called a sum-free set. The maximum size
                 of a sum-free set in the cyclic group {\mathbb{Z}}$_n$
                 was found almost 40 years ago by Diamanda and Yap; the
                 general case for arbitrary finite abelian groups was
                 recently settled by Green and Ruzsa. Here we find the
                 value of \lambda$_{3, 1}$ ({\mathbb{Z}}$_n$). More
                 generally, a recent paper by Hamidoune and Plagne
                 examines (k,l)-sum-free sets in G when $k - l$ and the
                 order of G are relatively prime; we extend their
                 results to see what happens without this assumption.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Luca:2009:MFP,
  author =       "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}",
  title =        "On {Machin}'s Formula with Powers of the {Golden}
                 Section",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "973--979",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002493",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002493",
  abstract =     "In this note, we find all solutions of the equation
                 \pi /4 = a arctan(\varphi$^{\kappa }$) + b
                 arctan(\varphi$^{\ell }$), in integers \kappa and \ell
                 and rational numbers a and b, where \varphi is the
                 golden section.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hegyvari:2009:ICL,
  author =       "Norbert Hegyv{\'a}ri and Fran{\c{c}}ois Hennecart and
                 Alain Plagne",
  title =        "Iterated Compositions of Linear Operations on Sets of
                 Positive Upper Density",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "981--997",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900250X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900250X",
  abstract =     "Starting from a result of Stewart, Tijdeman and Ruzsa
                 on iterated difference sequences, we introduce the
                 notion of iterated compositions of linear operations.
                 We prove a general result on the stability of such
                 compositions (with bounded coefficients) on sets of
                 integers having a positive upper density.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jones:2009:PVT,
  author =       "Lenny Jones",
  title =        "Polynomial Variations on a Theme of {Sierpi{\'n}ski}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "999--1015",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002511",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002511",
  abstract =     "In 1960, Sierpi{\'n}ski proved that there exist
                 infinitely many odd positive integers k such that k
                 \cdotp 2$^n$ + 1 is composite for all integers n \geq
                 0. Variations of this problem, using polynomials with
                 integer coefficients, and considering reducibility over
                 the rationals, have been investigated by several
                 authors. In particular, if S is the set of all positive
                 integers d for which there exists a polynomial f(x) \in
                 {\mathbb{Z}}[x], with f(1) \neq -d, such that f(x)x$^n$
                 + d is reducible over the rationals for all integers n
                 \geq 0, then what are the elements of S? Interest in
                 this problem stems partially from the fact that if S
                 contains an odd integer, then a question of Erd{\H{o}}s
                 and Selfridge concerning the existence of an odd
                 covering of the integers would be resolved. Filaseta
                 has shown that S contains all positive integers d
                 \equiv 0 (mod 4), and until now, nothing else was known
                 about the elements of S. In this paper, we show that S
                 contains infinitely many positive integers d \equiv 6
                 (mod 12). We also consider the corresponding problem
                 over {$ \mathbb {F} $}$_p$, and in that situation, we
                 show 1 \in S for all primes p.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baier:2009:PQP,
  author =       "Stephan Baier and Liangyi Zhao",
  title =        "On Primes in Quadratic Progressions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1017--1035",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002523",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002523",
  abstract =     "We verify the Hardy--Littlewood conjecture on primes
                 in quadratic progressions on average. The results in
                 the present paper significantly improve those of a
                 previous paper by the authors [3].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dubickas:2009:FPR,
  author =       "Art{\=u}ras Dubickas",
  title =        "On the Fractional Parts of Rational Powers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1037--1048",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002535",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002535",
  abstract =     "Let \xi be a non-zero real number, and let a = p/q > 1
                 be a rational number. We denote by U(a,\xi) and
                 L(a,\xi) the largest and the smallest limit points of
                 the sequence of fractional parts {\xi a$^n$ }, n =
                 0,1,2,\ldots, respectively. A possible way to prove
                 Mahler's conjecture claiming that Z-numbers do not
                 exist is to show that U(3/2,\xi) > 1/2 for every \xi >
                 0. We prove that U(3/2,\xi) cannot belong to [0,1/3)
                 \cup S, where S is an explicit infinite union of
                 intervals in (1/3,1/2). This result is a corollary to a
                 more general result claiming that, for any rational a >
                 1, U(a,\xi) cannot lie in a certain union of intervals.
                 We also obtain new inequalities for the difference
                 U(a,\xi) - L(a,\xi). Using them we show that some
                 analogues of Z-numbers do not exist.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Knopp:2009:ECG,
  author =       "Marvin Knopp and Joseph Lehner and Wissam Raji",
  title =        "{Eichler} Cohomology for Generalized Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1049--1059",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002547",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002547",
  abstract =     "By using Stokes's theorem, we prove an Eichler
                 cohomology theorem for generalized modular forms with
                 some restrictions on the relevant multiplier systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Katsurada:2009:DAA,
  author =       "Masanori Katsurada and Takumi Noda",
  title =        "Differential Actions on the Asymptotic Expansions of
                 Non-Holomorphic {Eisenstein} Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1061--1088",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002559",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002559",
  abstract =     "Let k be an arbitrary even integer, and E$_k$ (s;z)
                 denote the non-holomorphic Eisenstein series (of weight
                 k attached to SL$_2$ ({\mathbb{Z}})), defined by (1.1)
                 below. In the present paper we first establish a
                 complete asymptotic expansion of E$_k$ (s;z) in the
                 descending order of y as y \rightarrow + \infty
                 (Theorem 2.1), upon transferring from the previously
                 derived asymptotic expansion of E$_0$ (s;z) (due to the
                 first author [16]) to that of E$_k$ (s;z) through
                 successive use of Maass' weight change operators.
                 Theorem 2.1 yields various results on E$_k$ (s;z),
                 including its functional properties (Corollaries
                 2.1--2.3), its relevant specific values (Corollaries
                 2.4--2.7), and its asymptotic aspects as z \rightarrow
                 0 (Corollary 2.8). We then apply the non-Euclidean
                 Laplacian \Delta$_{H, k}$ (of weight k attached to the
                 upper-half plane) to the resulting expansion, in order
                 to justify the eigenfunction equation for E$_k$ (s;z)
                 in (1.6), where the justification can be made uniformly
                 in the whole s-plane (Theorem 2.2).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pong:2009:LSN,
  author =       "Wai Yan Pong",
  title =        "Length Spectra of Natural Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1089--1102",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002584",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002584",
  abstract =     "A natural number n can generally be written as a sum
                 of m consecutive natural numbers for various values of
                 m \geq 1. The length spectrum of n is the set of these
                 admissible m. Two numbers are spectral equivalent if
                 they have the same length spectrum. We show how to
                 compute the equivalence classes of this relation.
                 Moreover, we show that these classes can only have
                 either 1,2 or infinitely many elements.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pries:2009:TCL,
  author =       "Rachel Pries",
  title =        "The $p$-torsion of curves with large $p$-rank",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1103--1116",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002560",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002560",
  abstract =     "Consider the moduli space of smooth curves of genus g
                 and $p$-rank f defined over an algebraically closed
                 field k of characteristic p. It is an open problem to
                 classify which group schemes occur as the $p$-torsion
                 of the Jacobians of these curves for f < g - 1. We
                 prove that the generic point of every component of this
                 moduli space has a-number 1 when f = g - 2 and f = g -
                 3. Likewise, we show that a generic hyperelliptic curve
                 with $p$-rank g 2 has a-number 1 when p \geq 3. We also
                 show that the locus of curves with $p$-rank g - 2 and
                 a-number 2 is non-empty with codimension 3 in when p
                 \geq 5. We include some other results when f = g - 3.
                 The proofs are by induction on g while fixing g - f.
                 They use computations about certain components of the
                 boundary of.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Muriefah:2009:DE,
  author =       "Fadwa S. Abu Muriefah and Florian Luca and Samir
                 Siksek and Szabolcs Tengely",
  title =        "On the {Diophantine} equation {$ x^2 + C = 2 y^n $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1117--1128",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002572",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002572",
  abstract =     "In this paper, we study the Diophantine equation x$^2$
                 + C = 2y$^n$ in positive integers x,y with gcd(x,y) =
                 1, where n \geq 3 and C is a positive integer. If C
                 \equiv 1 (mod 4), we give a very sharp bound for prime
                 values of the exponent n; our main tool here is the
                 result on existence of primitive divisors in Lehmer
                 sequences due to Bilu, Hanrot and Voutier. We
                 illustrate our approach by solving completely the
                 equations x$^2$ + 17$^{a 1}$ = 2y$^n$, x$^2$ + 5$^{a
                 1}$ 13$^{a 2}$ = 2y$^n$ and x$^2$ + 3$^{a 1}$ 11$^{a
                 2}$ = 2y$^n$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chen:2009:GSP,
  author =       "Sin-Da Chen and Sen-Shan Huang",
  title =        "On General Series--Product Identities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "6",
  pages =        "1129--1148",
  month =        sep,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002596",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:20 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002596",
  abstract =     "We derive the general series--product identities from
                 which we deduce several applications, including an
                 identity of Gauss, the generalization of Winquist's
                 identity by Carlitz and Subbarao, an identity for, the
                 quintuple product identity, and the octuple product
                 identity.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Liu:2009:GRT,
  author =       "Yu-Ru Liu and Craig V. Spencer",
  title =        "A Generalization of {Roth}'s Theorem in Function
                 Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1149--1154",
  month =        nov,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109002602",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002602",
  abstract =     "Let {$ \mathbb {F} $}$_q$ [t] denote the polynomial
                 ring over the finite field {$ \mathbb {F} $}$_q$, and
                 let denote the subset of {$ \mathbb {F} $}$_q$ [t]
                 containing all polynomials of degree strictly less than
                 N. For non-zero elements r$_1$, \ldots, r$_s$ of {$
                 \mathbb {F} $}$_q$ satisfying r$_1$ + \cdots + r$_s$ =
                 0, let denote the maximal cardinality of a set which
                 contains no non-trivial solution of r$_1$ x$_1$ +
                 \cdots + r$_s$ x$_s$ = 0 with x$_i$ \in A (1 \leq i
                 \leq s). We prove that.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bayer-Fluckiger:2009:EMC,
  author =       "Eva Bayer-Fluckiger and Jean-Paul Cerri and
                 J{\'e}r{\^o}me Chaubert",
  title =        "{Euclidean} Minima and Central Division Algebras",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1155--1168",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002614",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002614",
  abstract =     "The notion of Euclidean minimum of a number field is a
                 classical one. In this paper, we generalize it to
                 central division algebras and establish some general
                 results in this new context.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Liu:2009:NLT,
  author =       "Huaning Liu",
  title =        "A note on {Lehmer} $k$-tuples",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1169--1178",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002626",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002626",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kuo:2009:GLD,
  author =       "Wentang Kuo and Yu-Ru Liu",
  title =        "{Gaussian} Laws on {Drinfeld} Modules",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1179--1203",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002638",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002638",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Belliard:2009:ACC,
  author =       "Jean-Robert Belliard",
  title =        "Asymptotic Cohomology of Circular Units",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1205--1219",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S179304210900264X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304210900264X",
  abstract =     "Let F be a number field, abelian over {$ \mathbb {Q}
                 $}, and fix a prime p \neq 2. Consider the cyclotomic
                 {\mathbb{Z}}$_p$-extension F$_{\infty }$ /F and denote
                 F$_n$ the nth finite subfield and C$_n$ its group of
                 circular units as defined by Sinnott. Then the Galois
                 groups G$_{m, n}$ = Gal(F$_m$ /F$_n$) act naturally on
                 the C$_m$ 's (for any m \geq n \gg 0). We compute the
                 Tate cohomology groups for i = -1,0 without assuming
                 anything else neither on F nor on p.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Olofsson:2009:LRH,
  author =       "Rikard Olofsson",
  title =        "Local {Riemann} Hypothesis for Complex Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1221--1230",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002651",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002651",
  abstract =     "In this paper, a special class of local \zeta
                 functions is studied. The main theorem states that the
                 functions have all zeros on the line {\mathfrak{R}}(s)
                 = 1/2. This is a natural generalization of the result
                 of Bump and Ng stating that the zeros of the Mellin
                 transform of Hermite functions have {\mathfrak{R}}(s) =
                 1/2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bundschuh:2009:ARC,
  author =       "Peter Bundschuh and Keijo V{\"a}{\"a}n{\"a}nen",
  title =        "Arithmetical results on certain $q$-series, {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1231--1245",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002663",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002663",
  abstract =     "As in Part I, entire transcendental solutions of
                 certain mth order linear q-difference equations are
                 investigated arithmetically, where now the polynomial
                 coefficients are much more general. The purpose of this
                 paper is to produce again lower bounds for the
                 dimension of the K-vector space generated by 1 and the
                 values of these solutions at m successive powers of q,
                 where K is the rational or an imaginary quadratic
                 field. A new feature in the proof is to use
                 simultaneously positive and negative powers of q as
                 interpolation points leading to an extra parameter in
                 the main result extending its applicability.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2009:COD,
  author =       "Ping-Shun Chan and Yuval Z. Flicker",
  title =        "Cyclic Odd Degree Base Change Lifting for Unitary
                 Groups in Three Variables",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1247--1309",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002687",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002687",
  abstract =     "Let F be a number field or a $p$-adic field of odd
                 residual characteristic. Let E be a quadratic extension
                 of F, and F' an odd degree cyclic field extension of F.
                 We establish a base-change functorial lifting of
                 automorphic (respectively, admissible) representations
                 from the unitary group U(3, E/F) to the unitary group
                 U(3, F' E/F'). As a consequence, we classify, up to
                 certain restrictions, the packets of U(3, F' E/F')
                 which contain irreducible automorphic (respectively,
                 admissible) representations invariant under the action
                 of the Galois group Gal(F' E/E). We also determine the
                 invariance of individual representations. This work is
                 the first study of base change into an algebraic group
                 whose packets are not all singletons, and which does
                 not satisfy the rigidity, or ``strong multiplicity
                 one'', theorem. Novel phenomena are encountered: e.g.
                 there are invariant packets where not every irreducible
                 automorphic (respectively, admissible) member is
                 Galois-invariant. The restriction that the residual
                 characteristic of the local fields be odd may be
                 removed once the multiplicity one theorem for U(3) is
                 proved to hold unconditionally without restriction on
                 the dyadic places.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alladi:2009:NCS,
  author =       "Krishnaswami Alladi",
  title =        "A new combinatorial study of the {Rogers--Fine}
                 identity and a related partial theta series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1311--1320",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002675",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002675",
  abstract =     "We provide a transparent combinatorial derivation of a
                 variant of the Rogers--Fine identity and a new
                 combinatorial proof of a related partial theta
                 series.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dummigan:2009:SSF,
  author =       "Neil Dummigan",
  title =        "Symmetric Square {$L$}-Functions and
                 {Shafarevich--Tate} Groups, {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "7",
  pages =        "1321--1345",
  month =        nov,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002699",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002699",
  abstract =     "We re-examine some critical values of symmetric square
                 {$L$}-functions for cusp forms of level one. We
                 construct some more of the elements of large prime
                 order in Shafarevich--Tate groups, demanded by the
                 Bloch--Kato conjecture. For this, we use the Galois
                 interpretation of Kurokawa-style congruences between
                 vector-valued Siegel modular forms of genus two (cusp
                 forms and Klingen--Eisenstein series), making further
                 use of a construction due to Urban. We must assume that
                 certain 4-dimensional Galois representations are
                 symplectic. Our calculations with Fourier expansions
                 use the Eholzer--Ibukiyama generalization of the
                 Rankin--Cohen brackets. We also construct some elements
                 of global torsion which should, according to the
                 Bloch--Kato conjecture, contribute a factor to the
                 denominator of the rightmost critical value of the
                 standard {$L$}-function of the Siegel cusp form. Then
                 we prove, under certain conditions, that the factor
                 does occur.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Toulmonde:2009:CAV,
  author =       "Vincent Toulmonde",
  title =        "Comportement au voisinage de $1$ de la fonction de
                 r{\'e}partition de $ \phi (n) / n$. ({French})
                 [{Behavior} in the neighborhood of $1$ of the partition
                 function $ \phi (n) / n $]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1347--1384",
  month =        dec,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042109001414",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109001414",
  abstract =     "Let \phi denote Euler's totient function, and G be the
                 distribution function of \phi (n)/n. Using functional
                 equations, it is shown that \phi (n)/n is statistically
                 close to 1 essentially when prime factors of n are
                 large. A function defined by a difference-differential
                 equation gives a quantitative measure of the
                 statistical influence of the size of prime factors of n
                 on the closeness of \phi (n)/n to 1. As a corollary, an
                 asymptotic expansion at any order of
                 G(1)-G(1-\varepsilon) is obtained according to negative
                 powers of log(1/\varepsilon), when \varepsilon tends to
                 0$^+$. This improves a result of Erd{\H{o}}s (1946) in
                 which he gives the first term of it. By optimally
                 choosing the order of this expansion, an estimation of
                 G(1)-G(1-\varepsilon) is deduced, involving an error
                 term of the same size as the best known error term
                 involved in prime number theorem. Soit \phi
                 l'indicatrice d'Euler. Nous {\'e}tudions le
                 comportement au voisinage de 1 de la fonction G de
                 r{\'e}partition de \phi (n)/n, via la mise en
                 {\'e}vidence d'{\'e}quations fonctionnelles. Nous
                 obtenons un r{\'e}sultat mesurant l'influence
                 statistique de la taille du plus petit facteur premier
                 d'un entier g{\'e}n{\'e}rique n quant {\`a} la
                 proximit{\'e} de \phi (n)/n par rapport {\`a} 1. Ce
                 r{\'e}sultat met en jeu une fonction d{\'e}finie par
                 une {\'e}quation diff{\'e}rentielle aux
                 diff{\'e}rences. Nous en d{\'e}duisons un
                 d{\'e}veloppement limit{\'e} {\`a} tout ordre de
                 G(1)-G(1-\varepsilon ) selon les puissances de 1/(log
                 1/\varepsilon), am{\'e}liorant ainsi un r{\'e}sultat
                 d'Erd{\H{o}}s (1946) dans lequel il obtient le premier
                 terme de ce d{\'e}veloppement. Une troncature
                 convenable de ce d{\'e}veloppement fournit un terme
                 d'erreur comparable {\`a} celui actuellement connu pour
                 le th{\'e}or{\`e}me des nombres premiers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Berkovich:2009:TPN,
  author =       "Alexander Berkovich",
  title =        "The Tri-Pentagonal Number Theorem and Related
                 Identities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1385--1399",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002705",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002705",
  abstract =     "I revisit an automated proof of Andrews' pentagonal
                 number theorem found by Riese. I uncover a simple
                 polynomial identity hidden behind his proof. I explain
                 how to use this identity to prove Andrews' result along
                 with a variety of new formulas of similar type. I
                 reveal an interesting relation between the
                 tri-pentagonal theorem and items (19), (20), (94), (98)
                 on the celebrated Slater list. Finally, I establish a
                 new infinite family of multiple series identities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ressler:2009:BQF,
  author =       "Wendell Ressler",
  title =        "On Binary Quadratic Forms and the {Hecke} Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1401--1418",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002730",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002730",
  abstract =     "We present a reduction theory for certain binary
                 quadratic forms with coefficients in
                 {\mathbb{Z}}[\lambda ], where \lambda is the minimal
                 translation in a Hecke group. We generalize from the
                 modular group \Gamma (1) = PSL(2,{\mathbb{Z}}) to the
                 Hecke groups and make extensive use of modified
                 negative continued fractions. We also define and
                 characterize ``reduced'' and ``simple'' hyperbolic
                 fixed points of the Hecke groups.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bell:2009:BSF,
  author =       "Jason P. Bell and Jonathan W. Bober",
  title =        "Bounded Step Functions and Factorial Ratio Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1419--1431",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002742",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002742",
  abstract =     "We study certain step functions whose nonnegativity is
                 related to the integrality of sequences of ratios of
                 factorial products. In particular, we obtain a lower
                 bound for the mean square of such step functions which
                 allows us to give a restriction on when such a
                 factorial ratio sequence can be integral. Additionally,
                 we note that this work has applications to the
                 classification of cyclic quotient singularities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{El-Guindy:2009:FEM,
  author =       "Ahmad El-Guindy",
  title =        "{Fourier} Expansions with Modular Form Coefficients",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1433--1446",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002717",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002717",
  abstract =     "In this paper, we study the Fourier expansion where
                 the coefficients are given as the evaluation of a
                 sequence of modular forms at a fixed point in the upper
                 half-plane. We show that for prime levels l for which
                 the modular curve X$_0$ (l) is hyperelliptic (with
                 hyperelliptic involution of the Atkin--Lehner type)
                 then one can choose a sequence of weight k (any even
                 integer) forms so that the resulting Fourier expansion
                 is itself a meromorphic modular form of weight 2-k.
                 These sequences have many interesting properties, for
                 instance, the sequence of their first nonzero
                 next-to-leading coefficient is equal to the terms in
                 the Fourier expansion of a certain weight 2-k form. The
                 results in the paper generalizes earlier work by Asai,
                 Kaneko, and Ninomiya (for level one), and Ahlgren (for
                 the cases where X$_0$ (l) has genus zero).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ehrenpreis:2009:EPS,
  author =       "Leon Ehrenpreis",
  title =        "{Eisenstein} and {Poincar{\'e}} Series on {$ \mathrm
                 {SL}(3, r) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1447--1475",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002729",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002729",
  abstract =     "This work continues the ideas presented in the
                 author's book, {\em The Universality of the Radon
                 Transform\/} (Oxford, 2003), which deals with the group
                 SL(2,R). The complication that arises for G = SL(3,R)
                 comes from the fact that there are now two fundamental
                 representations. This has the consequence that the wave
                 operator, which plays a central role in our work on
                 SL(2,R) is replaced by an overdetermined system of
                 partial differential equations. The analog of the wave
                 operator is defined using an MN invariant orbit of G
                 acting on the direct sum of the symmetric squares of
                 the fundamental representations. The relation of
                 orbits, or, in general, of any algebraic variety, to a
                 system of partial differential equations comes via the
                 Fundamental Principle, which shows how Fourier
                 transforms of functions or measures on an algebraic
                 variety correspond to solutions of the system of
                 partial differential equations defined by the equations
                 of the variety. In particular, we can start with the
                 sum T of the delta functions of the orbit of the group
                 \Gamma = SL(2,Z) on the light cone. We then take its
                 Fourier transform, using a suitable quadratic form. We
                 then decompose the Fourier transform under the
                 commuting group of G. In this way, we obtain a \Gamma
                 invariant distribution which has a natural restriction
                 to the orbit G/K, which is the symmetric space of G.
                 This restriction is (essentially) the nonanalytic
                 Eisenstein series. We can compute the periods of the
                 Eisenstein series over various orbits of subgroups of G
                 by means of the Euclidean Plancherel formula. A more
                 complicated form of these ideas is needed to define
                 Poincar{\'e} series.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Liu:2009:SFT,
  author =       "Zhi-Guo Liu and Xiao-Mei Yang",
  title =        "On the {Schr{\"o}ter} formula for theta functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1477--1488",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002754",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002754",
  abstract =     "The Schr{\"o}ter formula is an important theta
                 function identity. In this paper, we will point out
                 that some well-known addition formulas for theta
                 functions are special cases of the Schr{\"o}ter
                 formula. We further show that the Hirschhorn septuple
                 product identity can also be derived from this formula.
                 In addition, this formula allows us to derive four
                 remarkable theta functions identities, two of them are
                 extensions of two well-known Ramanujan's identities
                 related to the modular equations of degree 5. A
                 trigonometric identity is also proved.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2009:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 5)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "5",
  number =       "8",
  pages =        "1489--1493",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1142/S1793042109002766",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042109002766",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baoulina:2010:NSC,
  author =       "Ioulia Baoulina",
  title =        "On the Number of Solutions to Certain Diagonal
                 Equations Over Finite Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "1--14",
  month =        feb,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110002776",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002776",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Munshi:2010:DPR,
  author =       "Ritabrata Munshi",
  title =        "Density of Positive Rank Fibers in Elliptic
                 Fibrations, {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "15--23",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002867",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002867",
  abstract =     "We show that for a quartic elliptic fibration over a
                 real number field, existence of two positive rank
                 fibers implies existence of a dense set of positive
                 rank fibers. We also prove the same result for certain
                 sextic families.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Krieg:2010:TSH,
  author =       "Aloys Krieg",
  title =        "Theta Series Over the {Hurwitz} Quaternions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "25--36",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002788",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002788",
  abstract =     "There are six theta constants over the Hurwitz
                 quaternions on the quaternion half-space of degree 2.
                 The paper describes the behavior of these theta
                 constants under the transpose mapping, which can be
                 derived from the Fourier expansions. The results are
                 applied to the theta series of the first and second
                 kind.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alaca:2010:FOQ,
  author =       "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Kenneth S.
                 Williams",
  title =        "Fourteen Octonary Quadratic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "37--50",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000279X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000279X",
  abstract =     "We use the recent evaluation of certain convolution
                 sums involving the sum of divisors function to
                 determine the number of representations of a positive
                 integer by certain diagonal octonary quadratic forms
                 whose coefficients are 1, 2 or 4.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Beck:2010:FTC,
  author =       "Matthias Beck and Mary Halloran",
  title =        "Finite Trigonometric Character Sums Via Discrete
                 {Fourier} Analysis",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "51--67",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002806",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002806",
  abstract =     "We prove several old and new theorems about finite
                 sums involving characters and trigonometric functions.
                 These sums can be traced back to theta function
                 identities from Ramanujan's notebooks and were first
                 systematically studied by Berndt and Zaharescu where
                 their proofs involved complex contour integration. We
                 show how to prove most of Berndt--Zaharescu's and some
                 new identities by elementary methods of discrete
                 Fourier analysis.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Miller:2010:ATN,
  author =       "Alison Miller and Aaron Pixton",
  title =        "Arithmetic Traces of Non-Holomorphic Modular
                 Invariants",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "69--87",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002818",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002818",
  abstract =     "We extend results of Bringmann and Ono that relate
                 certain generalized traces of Maass--Poincar{\'e}
                 series to Fourier coefficients of modular forms of
                 half-integral weight. By specializing to cases in which
                 these traces are usual traces of algebraic numbers, we
                 generalize results of Zagier describing arithmetic
                 traces associated to modular forms. We define
                 correspondences and. We show that if f is a modular
                 form of non-positive weight 2 - 2 \lambda and odd level
                 N, holomorphic away from the cusp at infinity, then the
                 traces of values at Heegner points of a certain
                 iterated non-holomorphic derivative of f are equal to
                 Fourier coefficients of the half-integral weight
                 modular forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2010:CSA,
  author =       "Heng Huat Chan and Shaun Cooper and Francesco Sica",
  title =        "Congruences Satisfied by {Ap{\'e}ry}-Like Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "89--97",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002879",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002879",
  abstract =     "In this article, we investigate congruences satisfied
                 by Ap{\'e}ry-like numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hassen:2010:HZF,
  author =       "Abdul Hassen and Hieu D. Nguyen",
  title =        "Hypergeometric Zeta Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "99--126",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000282X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000282X",
  abstract =     "This paper investigates a new family of special
                 functions referred to as hypergeometric zeta functions.
                 Derived from the integral representation of the
                 classical Riemann zeta function, hypergeometric zeta
                 functions exhibit many properties analogous to their
                 classical counterpart, including the intimate
                 connection to Bernoulli numbers. These new properties
                 are treated in detail and are used to demonstrate a
                 functional inequality satisfied by second-order
                 hypergeometric zeta functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kane:2010:RIT,
  author =       "Ben Kane",
  title =        "Representations of Integers by Ternary Quadratic
                 Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "127--158",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002831",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002831",
  abstract =     "We investigate the representation of integers by
                 quadratic forms whose theta series lie in Kohnen's plus
                 space, where p is a prime. Conditional upon certain GRH
                 hypotheses, we show effectively that every sufficiently
                 large discriminant with bounded divisibility by p is
                 represented by the form, up to local conditions. We
                 give an algorithm for explicitly calculating the
                 bounds. For small p, we then use a computer to find the
                 full list of all discriminants not represented by the
                 form. Finally, conditional upon GRH for {$L$}-functions
                 of weight 2 newforms, we give an algorithm for
                 computing the implied constant of the
                 Ramanujan--Petersson conjecture for weight 3/2 cusp
                 forms of level 4N in Kohnen's plus space with N odd and
                 squarefree.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

%% Check page gap at publisher site: v6 n1 pp159--160
@Article{Bremner:2010:CST,
  author =       "Andrew Bremner and Blair K. Spearman",
  title =        "Cyclic sextic trinomials {$ x^6 + A x + B $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "161--167",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002843",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002843",
  abstract =     "A correspondence is obtained between irreducible
                 cyclic sextic trinomials x$^6$ + Ax + B \in {$ \mathbb
                 {Q}$}[x] and rational points on a genus two curve. This
                 implies that up to scaling, x$^6$ + 133x + 209 is the
                 only cyclic sextic trinomial of the given type.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Alaca:2010:SQF,
  author =       "Ay{\c{s}}e Alaca and {\c{S}}aban Alaca and Kenneth S.
                 Williams",
  title =        "Sextenary Quadratic Forms and an Identity of {Klein}
                 and {Fricke}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "169--183",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002880",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002880",
  abstract =     "Formulae, originally conjectured by Liouville, are
                 proved for the number of representations of a positive
                 integer n by each of the eight sextenary quadratic
                 forms, , , , , , , .",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Boylan:2010:APC,
  author =       "Matthew Boylan",
  title =        "Arithmetic Properties of Certain Level One {Mock}
                 Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "185--202",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002855",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002855",
  abstract =     "In a recent work, Bringmann and Ono [4] show that
                 Ramanujan's f(q) mock theta function is the holomorphic
                 projection of a harmonic weak Maass form of weight 1/2.
                 In this paper, we extend the work of Ono in [13]. In
                 particular, we study holomorphic projections of certain
                 integer weight harmonic weak Maass forms on SL$_2$
                 ({\mathbb{Z}}) using Hecke operators and the
                 differential theta-operator.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Copil:2010:RCP,
  author =       "Vlad Copil and Lauren{\c{t}}iu Panaitopol",
  title =        "On the Ratio of Consecutive Primes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "203--210",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002934",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002934",
  abstract =     "For n \geq 1, let p$_n$ be the nth prime number and
                 for n \geq 1. Using several results of Erd{\H{o}}s, we
                 study the sequence (q$_n$)$_{n \geq 1}$ and we prove
                 similar results as for the sequence (d$_n$)$_{n \geq
                 1}$, d$_n$ = p$_{n + 1}$- p$_n$. We also consider the
                 sequence for n \geq 1 and denote by G$_n$ and A$_n$ its
                 geometrical and arithmetical averages. We prove that
                 for n \geq 4.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Coons:2010:TSR,
  author =       "Michael Coons",
  title =        "The Transcendence of Series Related to {Stern}'s
                 Diatomic Sequence",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "1",
  pages =        "211--217",
  month =        feb,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002958",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:21 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002958",
  abstract =     "We prove various transcendence results regarding the
                 Stern sequence and related functions; in particular, we
                 prove that the generating function of the Stern
                 sequence is transcendental. Transcendence results are
                 also proven for the generating function of the Stern
                 polynomials and for power series whose coefficients
                 arise from some special subsequences of Stern's
                 sequence.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lagarias:2010:CSS,
  author =       "Jeffrey C. Lagarias",
  title =        "Cyclic Systems of Simultaneous Congruences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "219--245",
  month =        mar,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110002892",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See erratum \cite{Lagarias:2010:ECS}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002892",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kim:2010:BPQ,
  author =       "Sun Kim",
  title =        "A Bijective Proof of the Quintuple Product Identity",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "247--256",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002909",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002909",
  abstract =     "We give a bijective proof of the quintuple product
                 identity using bijective proofs of Jacobi's triple
                 product identity and Euler's recurrence relation.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bouallegue:2010:KNS,
  author =       "Kais Bouall{\`e}gue and Othman Echi and Richard G. E.
                 Pinch",
  title =        "{Korselt} Numbers and Sets",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "257--269",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002922",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002922",
  abstract =     "Let $ \alpha \in \mathbb {Z} \setminus {0} $. A
                 positive integer $N$ is said to be an $ \alpha
                 $-Korselt number ($ K_{\alpha }$-number, for short) if
                 $ N \neq \alpha $ and $ p \alpha $ divides $ N - \alpha
                 $ for each prime divisor $p$ of $N$. We are concerned,
                 here, with both a numerical and theoretical study of
                 composite squarefree Korselt numbers. The paper
                 contains two main results. The first one shows that for
                 $ \alpha \in \mathbb {Z} \setminus {0}$, the following
                 properties hold: (i) If $ \alpha \leq 1$, then each
                 composite squarefree $ K_{\alpha }$-number has at least
                 three prime factors. (ii) Suppose that $ \alpha > 1$.
                 Let $ p < q$ be two prime numbers and $ N \coloneq p
                 q$. If $N$ is an \alpha Korselt number, then $ p < q
                 \leq 4 \alpha - 3$. In particular, there are only
                 finitely many $ \alpha $ Korselt numbers with exactly
                 two prime factors. Let $ \alpha \in \mathbb {N}
                 \setminus {0}$; by an $ \alpha $-Williams number ($
                 W_{\alpha }$-number, for short) we mean a positive
                 integer which is both a $ K_{\alpha }$-number and a $
                 K_{- \alpha }$-number. Our second main result shows
                 that if $p$, $ 3 p - 2 $, $ 3 p + 2$ are all prime,
                 then their product is a ($ 3 p$)-Williams number.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kelmer:2010:DTK,
  author =       "Dubi Kelmer",
  title =        "Distribution of Twisted {Kloosterman} Sums Modulo
                 Prime Powers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "271--280",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002910",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002910",
  abstract =     "In this paper, we study Kloosterman sums twisted by
                 multiplicative characters modulo a prime power. We
                 show, by an elementary calculation, that these sums
                 become equidistributed on the real line with respect to
                 a suitable measure.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Garvan:2010:CAS,
  author =       "F. G. Garvan",
  title =        "Congruences for {Andrews}' Smallest Parts Partition
                 Function and New Congruences for {Dyson}'s Rank",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "281--309",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000296X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000296X",
  abstract =     "Let spt(n) denote the total number of appearances of
                 smallest parts in the partitions of n. Recently,
                 Andrews showed how spt(n) is related to the second rank
                 moment, and proved some surprising Ramanujan-type
                 congruences mod 5, 7 and 13. We prove a generalization
                 of these congruences using known relations between rank
                 and crank moments. We obtain explicit Ramanujan-type
                 congruences for spt(n) mod \ell for \ell = 11, 17, 19,
                 29, 31 and 37. Recently, Bringmann and Ono proved that
                 Dyson's rank function has infinitely many
                 Ramanujan-type congruences. Their proof is
                 non-constructive and utilizes the theory of weak Maass
                 forms. We construct two explicit nontrivial examples
                 mod 11 using elementary congruences between rank
                 moments and half-integer weight Hecke eigenforms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bennett:2010:DE,
  author =       "Michael A. Bennett and Jordan S. Ellenberg and Nathan
                 C. Ng",
  title =        "The {Diophantine} equation {$ A^4 + 2^\delta B^2 = C^n
                 $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "311--338",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002971",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002971",
  abstract =     "In a previous paper, the second author proved that the
                 equation $ A^4 + B^2 = C^p $ had no integral solutions
                 for prime $ p > 211 $ and $ (A, B, C) = 1 $. In the
                 present paper, we explain how to extend this result to
                 smaller exponents, and to the related equation $ A^4 +
                 2 B^2 = C^p $.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Souderes:2010:MDS,
  author =       "Ismael Soud{\`e}res",
  title =        "{Motivic} Double Shuffle",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "339--370",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002995",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002995",
  abstract =     "The goal of this paper is to give an elementary proof
                 of the double shuffle relations directly for the
                 Goncharov and Manin motivic multiple zeta values. The
                 shuffle relation is straightforward, but for the
                 stuffle, we use a modification of a method first
                 introduced by Cartier for the purpose of proving
                 stuffle for the real multiple zeta values. We will use
                 both the representation of multiple zeta values on the
                 moduli spaces of curve introduced by Goncharov and
                 Manin and we will apply suitable blow-up sequences to
                 the representation of multiple zeta values as integral
                 over a cube.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Han:2010:FNP,
  author =       "Jeong Soon Han and Hee Sik Kim and J. Neggers",
  title =        "The {Fibonacci}-Norm of a Positive Integer:
                 Observations and Conjectures",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "371--385",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003009",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See acknowledgement of priority \cite{Han:2011:APF}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003009",
  abstract =     "In this paper, we define the Fibonacci-norm of a
                 natural number n to be the smallest integer k such that
                 n|F$_k$, the kth Fibonacci number. We show that for m
                 \geq 5. Thus by analogy we say that a natural number n
                 \geq 5 is a local-Fibonacci-number whenever . We offer
                 several conjectures concerning the distribution of
                 local-Fibonacci-numbers. We show that, where provided
                 F$_{m + k}$ \equiv F$_m$ (mod n) for all natural
                 numbers m, with k \geq 1 the smallest natural number
                 for which this is true.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nebe:2010:LDS,
  author =       "Gabriele Nebe and Boris Venkov",
  title =        "Low-Dimensional Strongly Perfect Lattices. {III}: Dual
                 Strongly Perfect Lattices of Dimension $ 14 $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "387--409",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003022",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003022",
  abstract =     "A lattice is called dual strongly perfect if both, the
                 lattice and its dual, are strongly perfect. We show
                 that the extremal 3-modular lattice [\pm G$_2$
                 (3)]$_{14}$ with automorphism group C$_2$ $ \times $
                 G$_2$ ({$ \mathbb {F} $}$_3$) is the unique dual
                 strongly perfect lattice of dimension 14.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vulakh:2010:MBI,
  author =       "L. Ya. Vulakh",
  title =        "Minima of Binary Indefinite {Hermitian} Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "411--435",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003034",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003034",
  abstract =     "Classification of binary indefinite primitive
                 Hermitian forms modulo the action of the extended
                 Bianchi group (or Hilbert modular group) B$_d$ is
                 given. When the discriminant of the quadratic field
                 (and d) is negative, the results obtained can be
                 applied to classify the maximal non-elementary Fuchsian
                 subgroups of B$_d$, and to find the Hermitian points in
                 the Markov spectrum of B$_d$. If \nu is a Hermitian
                 point in the spectrum, then there is a set of extremal
                 geodesics in H$^3$, the upper half-space model of the
                 three-dimensional hyperbolic space, with diameter
                 1/\nu, which depends on one continuous parameter.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zhao:2010:EDP,
  author =       "Yusheng Zhao and Wei Li and Xianke Zhang",
  title =        "Effective Determination of Prime Decompositions of
                 Cubic Function Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "437--448",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110002983",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002983",
  abstract =     "In this paper, we determine completely the prime
                 decomposition of cubic function fields by effective and
                 explicit methods.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kim:2010:CPC,
  author =       "Byungchan Kim",
  title =        "Combinatorial Proofs of Certain Identities Involving
                 Partial Theta Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "2",
  pages =        "449--460",
  month =        mar,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003046",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003046",
  abstract =     "In this brief note, we give combinatorial proofs of
                 two identities involving partial theta functions. As an
                 application, we prove an identity for the product of
                 partial theta functions, first established by Andrews
                 and Warnaar. We also provide a generalization of the
                 first two identities and give a combinatorial proof of
                 the generalized identities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{McCarthy:2010:HSP,
  author =       "Dermot McCarthy",
  title =        "{$_3 F_2$} Hypergeometric Series and Periods of
                 Elliptic Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "461--470",
  month =        may,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110002946",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110002946",
  abstract =     "We express the real period of a family of elliptic
                 curves in terms of classical hypergeometric series.
                 This expression is analogous to a result of Ono which
                 relates the trace of Frobenius of the same family of
                 elliptic curves to a Gaussian hypergeometric series.
                 This analogy provides further evidence of the interplay
                 between classical and Gaussian hypergeometric series.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Viada:2010:LBN,
  author =       "Evelina Viada",
  title =        "Lower Bounds for the Normalized Height and Non-Dense
                 Subsets of Subvarieties of {Abelian} Varieties",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "471--499",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003010",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003010",
  abstract =     "This work is the third part of a series of papers. In
                 the first two, we considered curves and varieties in a
                 power of an elliptic curve. Here, we deal with
                 subvarieties of an abelian variety in general. Let V be
                 a proper irreducible subvariety of dimension d in an
                 abelian variety A, both defined over the algebraic
                 numbers. We say that V is weak-transverse if V is not
                 contained in any proper algebraic subgroup of A, and
                 transverse if it is not contained in any translate of
                 such a subgroup. Assume a conjectural lower bound for
                 the normalized height of V. Then, for V transverse, we
                 prove that the algebraic points of bounded height of V
                 which lie in the union of all algebraic subgroups of A
                 of codimension at least d + 1 translated by the points
                 close to a subgroup \Gamma of finite rank, are
                 non-Zariski-dense in V. If \Gamma has rank zero, it is
                 sufficient to assume that V is weak-transverse. The
                 notion of closeness is defined using a height
                 function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Borwein:2010:DTM,
  author =       "Jonathan M. Borwein and O-Yeat Chan",
  title =        "Duality in tails of multiple-zeta values",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "501--514",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003058",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11M32 (33C20 33F05)",
  MRnumber =     "2652893",
  MRreviewer =   "Zhonghua Li",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1218/;
                 https://www.worldscientific.com/doi/10.1142/S1793042110003058",
  abstract =     "Duality relations are deduced for tails of
                 multiple-zeta values using elementary methods. These
                 formulas extend the classical duality formulas for
                 multiple-zeta values.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2010:DTM",
}

@Article{Chu:2010:BBL,
  author =       "Wenchang Chu and Wenlong Zhang",
  title =        "Bilateral {Bailey} Lemma and False Theta Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "515--577",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000306X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000306X",
  abstract =     "By examining the transformation formulae between
                 unilateral series and bilateral ones derived from the
                 bilateral Bailey lemma, we establish numerous
                 identities of false theta functions, including most of
                 the known ones discovered mainly by Rogers [40] and
                 Ramanujan in his \booktitle{Lost Notebook} [39].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Fehm:2010:RAV,
  author =       "Arno Fehm and Sebastian Petersen",
  title =        "On the Rank of {Abelian} Varieties Over Ample Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "579--586",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003071",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003071",
  abstract =     "A field K is called ample if every smooth K-curve that
                 has a K-rational point has infinitely many of them. We
                 prove two theorems to support the following conjecture,
                 which is inspired by classical infinite rank results:
                 Every non-zero Abelian variety A over an ample field K
                 which is not algebraic over a finite field has infinite
                 rank. First, the {\mathbb{Z}}$_{(p)}$-module A(K)
                 \otimes {\mathbb{Z}}$_{(p)}$ is not finitely generated,
                 where p is the characteristic of K. In particular, the
                 conjecture holds for fields of characteristic zero.
                 Second, if K is an infinite finitely generated field
                 and S is a finite set of local primes of K, then every
                 Abelian variety over K acquires infinite rank over
                 certain subfields of the maximal totally S-adic Galois
                 extension of K. This strengthens a recent infinite rank
                 result of Geyer and Jarden.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bugeaud:2010:PRS,
  author =       "Yann Bugeaud and Maurice Mignotte",
  title =        "Polynomial Root Separation",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "587--602",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003083",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003083",
  abstract =     "We discuss the following question: How close to each
                 other can two distinct roots of an integer polynomial
                 be? We summarize what is presently known on this and
                 related problems, and establish several new results on
                 root separation of monic, integer polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ruhl:2010:AIQ,
  author =       "Klaas-Tido R{\"u}hl",
  title =        "Annihilating Ideals of Quadratic Forms Over Local and
                 Global Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "603--624",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003095",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003095",
  abstract =     "We study annihilating polynomials and annihilating
                 ideals for elements of Witt rings for groups of
                 exponent 2. With the help of these results and certain
                 calculations involving the Clifford invariant, we are
                 able to give full sets of generators for the
                 annihilating ideal of both the isometry class and the
                 equivalence class of an arbitrary quadratic form over a
                 local field. By applying the Hasse--Minkowski theorem,
                 we can then achieve the same for an arbitrary quadratic
                 form over a global field.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Le:2010:APT,
  author =       "Daniel Le and Shelly Manber and Shrenik Shah",
  title =        "On $p$-adic properties of twisted traces of singular
                 moduli",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "625--653",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003101",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003101",
  abstract =     "We prove that logarithmic derivatives of certain
                 twisted Hilbert class polynomials are holomorphic
                 modular forms modulo p of filtration p + 1. We derive
                 $p$-adic information about twisted Hecke traces and
                 Hilbert class polynomials. In this framework, we
                 formulate a precise criterion for $p$-divisibility of
                 class numbers of imaginary quadratic fields in terms of
                 the existence of certain cusp forms modulo p. We
                 explain the existence of infinite classes of congruent
                 twisted Hecke traces with fixed discriminant in terms
                 of the factorization of the associated Hilbert class
                 polynomial modulo p. Finally, we provide a new proof of
                 a theorem of Ogg classifying those p for which all
                 supersingular j-invariants modulo p lie in F$_p$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Haynes:2010:NDN,
  author =       "Alan K. Haynes",
  title =        "Numerators of Differences of Nonconsecutive {Farey}
                 Fractions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "655--666",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003113",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003113",
  abstract =     "An elementary but useful fact is that the numerator of
                 the difference of two consecutive Farey fractions is
                 equal to one. For triples of consecutive fractions, the
                 numerators of the differences are well understood and
                 have applications to several interesting problems. In
                 this paper, we investigate numerators of differences of
                 fractions which are farther apart. We establish
                 algebraic identities between such differences which
                 then allow us to calculate their average values by
                 using properties of a measure preserving transformation
                 of the Farey triangle.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Witno:2010:EPP,
  author =       "Amin Witno",
  title =        "On Elite Primes of Period Four",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "667--671",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003149",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003149",
  abstract =     "A prime p is elite if all sufficiently large Fermat
                 numbers F$_n$ = 2$^{2 n}$ + 1 are quadratic nonresidues
                 modulo p. In contrast, p is anti-elite if all
                 sufficiently large F$_n$ are quadratic residues modulo
                 p. The sequence F$_n$ modulo p is necessarily periodic.
                 We give a sequence of pairwise coprime integers whose
                 prime factors are each elite or anti-elite with period
                 four.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2010:RCCa,
  author =       "Hei-Chi Chan",
  title =        "{Ramanujan}'s cubic continued fraction and an analog
                 of his ``{Most Beautiful Identity}''",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "673--680",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003150",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003150",
  abstract =     "In this paper, we prove an analog of Ramanujan's
                 ``Most Beautiful Identity''. This analog is closely
                 related to Ramanujan's beautiful results involving the
                 cubic continued fraction.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chao:2010:NBS,
  author =       "Kuok Fai Chao and Roger Plymen",
  title =        "A new bound for the smallest $x$ with $ \pi (x) > \li
                 (x)$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "681--690",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003125",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003125",
  abstract =     "We reduce the leading term in Lehman's theorem. This
                 improved estimate allows us to refine the main theorem
                 of Bays and Hudson [2]. Entering 2,000,000 Riemann
                 zeros, we prove that there exists x in the interval
                 [exp (727.951858), exp (727.952178)] for which \pi (x)
                 - li(x) > 3.2 $ \times $ 10$^{151}$. There are at least
                 10$^{154}$ successive integers x in this interval for
                 which \pi (x) > li(x). This interval is strictly a
                 sub-interval of the interval in Bays and Hudson, and is
                 narrower by a factor of about 12.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kida:2010:CBQ,
  author =       "Masanari Kida and Y{\=u}ichi Rikuna and Atsushi Sato",
  title =        "Classifying {Brumer}'s Quintic Polynomials by Weak
                 {Mordell--Weil} Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "691--704",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003162",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003162",
  abstract =     "We develop a general classification theory for
                 Brumer's dihedral quintic polynomials by means of
                 Kummer theory arising from certain elliptic curves. We
                 also give a similar theory for cubic polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lalin:2010:CB,
  author =       "Matilde N. Lal{\'i}n",
  title =        "On a Conjecture by {Boyd}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "705--711",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003174",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003174",
  abstract =     "The aim of this note is to prove the Mahler measure
                 identity m(x + x$^{-1}$ + y + y$^{-1}$ + 5) = 6m(x +
                 x$^{-1}$ + y + y$^{-1}$ + 1) which was conjectured by
                 Boyd. The proof is achieved by proving relationships
                 between regulators of both curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vulakh:2010:HPM,
  author =       "L. Ya Vulakh",
  title =        "{Hermitian} Points in {Markov} Spectra",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "713--730",
  month =        jun,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110003186",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003186",
  abstract =     "Let H$^n$ be the upper half-space model of the
                 n-dimensional hyperbolic space. For n=3, Hermitian
                 points in the Markov spectrum of the extended Bianchi
                 group B$_d$ are introduced for any d. If \nu is a
                 Hermitian point in the spectrum, then there is a set of
                 extremal geodesics in H$^3$ with diameter 1/\nu, which
                 depends on one continuous parameter. It is shown that
                 \nu$^2$ \leq |D|/24 for any imaginary quadratic field
                 with discriminant D, whose ideal-class group contains
                 no cyclic subgroup of order 4, and in many other cases.
                 Similarly, in the case of n = 4, if \nu is a Hermitian
                 point in the Markov spectrum for SV(Z$^4$), some
                 discrete group of isometries of H$^4$, then the
                 corresponding set of extremal geodesics depends on two
                 continuous parameters.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vulakh:2010:DAI,
  author =       "L. Ya. Vulakh",
  title =        "{Diophantine} Approximation in Imaginary Quadratic
                 Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "731--766",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003137",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003137",
  abstract =     "Let H$^3$ be the upper half-space model of the
                 three-dimensional hyperbolic space. For certain
                 cocompact Fuchsian subgroups \Gamma of an extended
                 Bianchi group B$_d$, the extremality of the axis of
                 hyperbolic F \in \Gamma in H$_3$ with respect to \Gamma
                 implies its extremality with respect to B$_d$. This
                 reduction is used to obtain sharp lower bounds for the
                 Hurwitz constants and lower bounds for the highest
                 limit points in the Markov spectra of B$_d$ for some d
                 < 1000. In particular, such bounds are found for all
                 non-Euclidean class one imaginary quadratic fields. The
                 Hurwitz constants for the imaginary quadratic fields
                 with discriminants -120 and -132 are given. The second
                 minima are also indicated for these fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ganguly:2010:DSC,
  author =       "Satadal Ganguly",
  title =        "On the Dimension of the Space of Cusp Forms of
                 Octahedral Type",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "767--783",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003198",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003198",
  abstract =     "For a prime q \equiv 3 (mod 4) and the character, we
                 consider the subspace of the space of holomorphic cusp
                 forms of weight one, level q and character \chi that is
                 spanned by forms that correspond to Galois
                 representations of octahedral type. We prove that this
                 subspace has dimension bounded by upto multiplication
                 by a constant that depends only on \varepsilon.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rowell:2010:NEL,
  author =       "Michael Rowell",
  title =        "A New Exploration of the {Lebesgue} Identity",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "785--798",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003204",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003204",
  abstract =     "We introduce a new combinatorial proof of the Lebesgue
                 identity which allows us to find a new finite form of
                 the identity. Using this new finite form we are able to
                 make new observations about special cases of the
                 Lebesgue identity, namely the ``little'' G{\"o}llnitz
                 theorems and Sylvester's identity.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lev:2010:ABA,
  author =       "Vsevolod F. Lev and Mikhail E. Muzychuk and Rom
                 Pinchasi",
  title =        "Additive Bases in {Abelian} Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "799--809",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003216",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003216",
  abstract =     "Let G be a finite, non-trivial Abelian group of
                 exponent m, and suppose that B$_1$, \ldots, B$_k$ are
                 generating subsets of G. We prove that if k > 2m ln
                 log$_2$ |G|, then the multiset union B$_1$ \cup B$_k$
                 forms an additive basis of G; that is, for every g \in
                 G, there exist A$_1$ \subseteq B$_1$, \ldots, A$_k$
                 \subseteq B$_k$ such that. This generalizes a result of
                 Alon, Linial and Meshulam on the additive bases
                 conjecture. As another step towards proving the
                 conjecture, in the case where B$_1$, \ldots, B$_k$ are
                 finite subsets of a vector space, we obtain lower-bound
                 estimates for the number of distinct values, attained
                 by the sums of the form, where A$_i$ vary over all
                 subsets of B$_i$ for each i = 1,\ldots, k. Finally, we
                 establish a surprising relation between the additive
                 bases conjecture and the problem of covering the
                 vertices of a unit cube by translates of a lattice, and
                 present a reformulation of (the strong form of) the
                 conjecture in terms of coverings.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Volkov:2010:ASS,
  author =       "Maja Volkov",
  title =        "{Abelian} Surfaces with Supersingular Good Reduction
                 and Non-Semisimple {Tate} Module",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "811--818",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003228",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003228",
  abstract =     "We show the existence of abelian surfaces over {$
                 \mathbb {Q} $}$_p$ having good reduction with
                 supersingular special fiber whose associated $p$-adic
                 Galois module is not semisimple.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2010:RCCb,
  author =       "Hei-Chi Chan",
  title =        "{Ramanujan}'s Cubic Continued Fraction and {Ramanujan}
                 Type Congruences for a Certain Partition Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "819--834",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003241",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003241",
  abstract =     "In this paper, we study the divisibility of the
                 function a(n) defined by. In particular, we prove
                 certain ``Ramanujan type congruences'' for a(n) modulo
                 powers of 3.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sinick:2010:RCC,
  author =       "Jonah Sinick",
  title =        "{Ramanujan} Congruences for a Class of Eta Quotients",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "835--847",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003253",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003253",
  abstract =     "We consider a class of generating functions analogous
                 to the generating function of the partition function
                 and establish a bound on the primes \ell for which
                 their coefficients c(n) obey congruences of the form
                 c(\ell n + a) \equiv 0 (mod \ell). We apply this result
                 to obtain a complete characterization of the
                 congruences of the same form that the sequences c$_N$
                 (n) satisfy, where c$_N$ (n) is defined by. This last
                 result answers a question of H.-C. Chan.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Xia:2010:BNC,
  author =       "Binzhou Xia and Tianxin Cai",
  title =        "{Bernoulli} Numbers and Congruences for Harmonic
                 Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "849--855",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003265",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003265",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Brown:2010:FNH,
  author =       "Jim Brown",
  title =        "The first negative {Hecke} eigenvalue of genus $2$
                 {Siegel} cuspforms with level $ n \geq 1$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "857--867",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003277",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003277",
  abstract =     "In this short paper, we extend results of Kohnen and
                 Sengupta on the sign of eigenvalues of Siegel
                 cuspforms. We show that their bound for the first
                 negative Hecke eigenvalue of a genus 2 Siegel cuspform
                 of level 1 extends to the case of level N > 1. We also
                 discuss the signs of Hecke eigenvalues of CAP forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Williams:2010:UIC,
  author =       "Gerald Williams",
  title =        "Unimodular Integer Circulants Associated with
                 Trinomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "869--876",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003289",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003289",
  abstract =     "The n $ \times $ n circulant matrix associated with
                 the polynomial (with d < n) is the one with first row
                 (a$_0$ \cdots a$_d$ 0 \cdots 0). The problem as to when
                 such circulants are unimodular arises in the theory of
                 cyclically presented groups and leads to the following
                 question, previously studied by Odoni and Cremona: when
                 is Res(f(t), t$^n$-1) = \pm 1? We give a complete
                 answer to this question for trinomials f(t) = t$^m$ \pm
                 t$^k$ \pm 1. Our main result was conjectured by the
                 author in an earlier paper and (with two exceptions)
                 implies the classification of the finite
                 Cavicchioli--Hegenbarth--Repov{\v{s}} generalized
                 Fibonacci groups, thus giving an almost complete answer
                 to a question of Bardakov and Vesnin.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ahmadi:2010:MOG,
  author =       "Omran Ahmadi and Igor E. Shparlinski and Jos{\'e}
                 Felipe Voloch",
  title =        "Multiplicative Order of {Gauss} Periods",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "877--882",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003290",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003290",
  abstract =     "We obtain a lower bound on the multiplicative order of
                 Gauss periods which generate normal bases over finite
                 fields. This bound improves the previous bound of von
                 zur Gathen and Shparlinski.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Balazard:2010:CBD,
  author =       "Michel Balazard and Anne {De Roton}",
  title =        "Sur un crit{\`e}re de {B{\'a}ez--Duarte} pour
                 l'hypoth{\`e}se de {Riemann}. ({French}) [{On} a
                 criterion of {B{\'a}ez--Duarte} for the {Riemann
                 Hypothesis}]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "883--903",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003307",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003307",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Maier:2010:ESP,
  author =       "H. Maier and A. Sankaranarayanan",
  title =        "Exponential Sums Over Primes in Residue Classes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "905--918",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003319",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003319",
  abstract =     "We specialize a problem studied by Elliott, the
                 behavior of arbitrary sequences a$_p$ of complex
                 numbers on residue classes to prime moduli to the case
                 a$_p$ = e(\alpha p). For these special cases, we obtain
                 under certain additional conditions improvements on
                 Elliott's results.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Roy:2010:SVE,
  author =       "Damien Roy",
  title =        "Small Value Estimates for the Additive Group",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "919--956",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000323X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000323X",
  abstract =     "We generalize Gel'fond's criterion for algebraic
                 independence to the context of a sequence of
                 polynomials whose first derivatives take small values
                 on large subsets of a fixed subgroup of $ \mathbb {C}
                 $, instead of just one point (one extension deals with
                 a subgroup of $ \mathbb {C}^\times $).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lagarias:2010:ECS,
  author =       "Jeffrey C. Lagarias",
  title =        "Erratum: {``Cyclic Systems of Simultaneous
                 Congruences''}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "4",
  pages =        "??--??",
  month =        jun,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003320",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:22 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See \cite{Lagarias:2010:CSS}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003320",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jouhet:2010:IEI,
  author =       "Fr{\'e}d{\'e}ric Jouhet and Elie Mosaki",
  title =        "Irrationalit{\'e} aux entiers impairs positifs d'un
                 $q$-analogue de la fonction z{\^e}ta de {Riemann}.
                 ({French}) [{Irrationality} to positive odd integers of
                 a $q$-analogue of the {Riemann} zeta function]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "959--988",
  month =        aug,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110003332",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003332",
  abstract =     "Dans cet article, nous nous int{\'e}ressons {\`a} un
                 q-analogue aux entiers positifs de la fonction z{\^e}ta
                 de Riemann, que l'on peut {\'e}crire pour s \in
                 \mathbb{N} * sous la forme \zeta$_q$ (s) = $ \sum_{k
                 \geq 1}$ q$^k$ $ \sum_{d|k}$ d$^{s - 1}$. Nous donnons
                 une nouvelle minoration de la dimension de l'espace
                 vectoriel sur {$ \mathbb {Q}$} engendr{\'e}, pour 1/q
                 \in {\mathbb{Z}}{-1; 1} et A entier pair, par 1,
                 \zeta$_q$ (3), \zeta$_q$ (5), \ldots, \zeta$_q$ (A -
                 1). Ceci am{\'e}liore un r{\'e}sultat r{\'e}cent de
                 Krattenthaler, Rivoal et Zudilin ([13]). En particulier
                 notre r{\'e}sultat a pour cons{\'e}quence le fait que
                 pour 1/q \in {\mathbb{Z}}{-1; 1}, au moins l'un des
                 nombres \zeta$_q$ (3), \zeta$_q$ (5), \zeta$_q$ (7),
                 \zeta$_q$ (9) est irrationnel. In this paper, we focus
                 on a q-analogue of the Riemann zeta function at
                 positive integers, which can be written for s \in
                 \mathbb{N} * by \zeta$_q$ (s) = $ \sum_{k \geq 1}$
                 q$^k$ $ \sum_{d|k}$ d$^{s - 1}$. We give a new lower
                 bound for the dimension of the vector space over {$
                 \mathbb {Q}$} spanned, for 1/q \in {\mathbb{Z}}{-1; 1}
                 and an even integer A, by 1, \zeta$_q$ (3), \zeta$_q$
                 (5), \ldots, \zeta$_q$ (A-1). This improves a recent
                 result of Krattenthaler, Rivoal and Zudilin ([13]). In
                 particular, a consequence of our result is that for 1/q
                 \in {\mathbb{Z}}{-1; 1}, at least one of the numbers
                 \zeta$_q$ (3), \zeta$_q$ (5), \zeta$_q$ (7), \zeta$_q$
                 (9) is irrational.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Hasegawa:2010:AOT,
  author =       "Takehiro Hasegawa",
  title =        "On Asymptotically Optimal Towers Over Quadratic Fields
                 Related to {Gauss} Hypergeometric Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "989--1009",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003344",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003344",
  abstract =     "We define two asymptotically optimal towers over
                 quadratic fields, and give the explicit descriptions of
                 the ramification loci and the sets of places splitting
                 completely, which relate to the elliptic modular curves
                 X$_0$ (4$^n$) and X$_0$ (3$^n$ ), respectively.
                 Moreover, in the last section, we determine completely
                 the modularity of a tower given by Maharaj and
                 Wulftange in [18].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ih:2010:FPP,
  author =       "Su-Ion Ih and Thomas J. Tucker",
  title =        "A Finiteness Property for Preperiodic Points of
                 {Chebyshev} Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1011--1025",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003356",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003356",
  abstract =     "Let K be a number field with algebraic closure, let S
                 be a finite set of places of K containing the
                 Archimedean places, and let \phi be a Chebyshev
                 polynomial. We prove that if is not preperiodic, then
                 there are only finitely many preperiodic points which
                 are S-integral with respect to \alpha.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gottesman:2010:QRP,
  author =       "Richard Gottesman and Kwokfung Tang",
  title =        "Quadratic Recurrences with a Positive Density of Prime
                 Divisors",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1027--1045",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003368",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003368",
  abstract =     "For f(x) \in {\mathbb{Z}}[x] and a \in {\mathbb{Z}},
                 we let f$^n$ (x) be the nth iterate of f(x), P(f, a) =
                 {p prime: p|f$^n$ (a) for some n}, and D(P(f, a))
                 denote the natural density of P(f, a) within the set of
                 primes. A conjecture of Jones [5] indicates that D(P(f,
                 a)) = 0 for most quadratic f. In this paper, we find an
                 exceptional family of (f, a) such that D(P(f, a)) > 0
                 by considering f$_t$ (x) = (x + t)$^2$- 2 - t and a$_t$
                 = f$_t$ (0) for t \in {\mathbb{Z}}. We prove that if t
                 is not of the form \pm M$^2$ \pm 2 or \pm 2M$^2$ \pm 2,
                 then D(P(f$_t$, a$_t$)) = {\u{2}153}. We also determine
                 D(P(f$_t$, a$_t$)) in some cases when the density is
                 not equal to {\u{2}153}. Our results suggest a
                 connection between the arithmetic dynamics of the
                 conjugates of x$^2$ and the conjugates of x$^2$- 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hoshi:2010:FIP,
  author =       "Akinari Hoshi and Katsuya Miyake",
  title =        "On the Field Intersection Problem of Solvable Quintic
                 Generic Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1047--1081",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000337X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000337X",
  abstract =     "We study a general method of the field intersection
                 problem of generic polynomials over an arbitrary field
                 k via formal Tschirnhausen transformation. In the case
                 of solvable quintic, we give an explicit answer to the
                 problem by using multi-resolvent polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Knopp:2010:ECG,
  author =       "Marvin Knopp and Wissam Raji",
  title =        "{Eichler} Cohomology for Generalized Modular Forms
                 {II}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1083--1090",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000340X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000340X",
  abstract =     "We derive further results on Eichler cohomology of
                 generalized modular forms of arbitrary real weight.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Agashe:2010:SSV,
  author =       "Amod Agashe",
  title =        "Squareness in the Special {$L$}-Value and Special
                 {$L$}-Values of Twists",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1091--1111",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003393",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003393",
  abstract =     "Let N be a prime and let A be a quotient of J$_0$ (N)
                 over Q associated to a newform such that the special
                 $L$-value of A (at s = 1) is non-zero. Suppose that the
                 algebraic part of the special $L$-value of A is
                 divisible by an odd prime q such that q does not divide
                 the numerator of. Then the Birch and Swinnerton-Dyer
                 conjecture predicts that the $q$-adic valuations of the
                 algebraic part of the special $L$-value of A and of the
                 order of the Shafarevich--Tate group are both positive
                 even numbers. Under a certain mod q non-vanishing
                 hypothesis on special $L$-values of twists of A, we
                 show that the $q$-adic valuations of the algebraic part
                 of the special $L$-value of A and of the Birch and
                 Swinnerton-Dyer conjectural order of the
                 Shafarevich--Tate group of A are both positive even
                 numbers. We also give a formula for the algebraic part
                 of the special $L$-value of A over quadratic imaginary
                 fields K in terms of the free abelian group on
                 isomorphism classes of supersingular elliptic curves in
                 characteristic N (equivalently, over conjugacy classes
                 of maximal orders in the definite quaternion algebra
                 over Q ramified at N and \infty) which shows that this
                 algebraic part is a perfect square up to powers of the
                 prime two and of primes dividing the discriminant of K.
                 Finally, for an optimal elliptic curve of arbitrary
                 conductor E, we give a formula for the special
                 $L$-value of the twist E$_{-D}$ of E by a negative
                 fundamental discriminant -D, which shows that this
                 special $L$-value is an integer up to a power of 2,
                 under some hypotheses. In view of the second part of
                 the Birch and Swinnerton-Dyer conjecture, this leads us
                 to the surprising conjecture that the square of the
                 order of the torsion subgroup of E$_{-D}$ divides the
                 product of the order of the Shafarevich--Tate group of
                 E$_{-D}$ and the orders of the arithmetic component
                 groups of E$_{-D}$, under certain mild hypotheses.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Matomaki:2010:NSN,
  author =       "Kaisa Matom{\"a}ki",
  title =        "A Note on Smooth Numbers in Short Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1113--1116",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003381",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003381",
  abstract =     "We prove that, for any \in > 0, there exists a
                 constant C > 0 such that the interval contains numbers
                 whose all prime factors are smaller than.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Shemanske:2010:CSH,
  author =       "T. Shemanske and S. Treneer and L. Walling",
  title =        "Constructing Simultaneous {Hecke} Eigenforms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1117--1137",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003411",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003411",
  abstract =     "It is well known that newforms of integral weight are
                 simultaneous eigenforms for all the Hecke operators,
                 and that the converse is not true. In this paper, we
                 give a characterization of all simultaneous Hecke
                 eigenforms associated to a given newform, and provide
                 several applications. These include determining the
                 number of linearly independent simultaneous eigenforms
                 in a fixed space which correspond to a given newform,
                 and characterizing several situations in which the full
                 space of cusp forms is spanned by a basis consisting of
                 such eigenforms. Part of our results can be seen as a
                 generalization of results of Choie--Kohnen who
                 considered diagonalization of ``bad'' Hecke operators
                 on spaces with square-free level and trivial character.
                 Of independent interest, but used herein, is a lower
                 bound for the dimension of the space of newforms with
                 arbitrary character.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kleinbock:2010:MDA,
  author =       "Dmitry Kleinbock and Gregory Margulis and Junbo Wang",
  title =        "Metric {Diophantine} Approximation for Systems of
                 Linear Forms Via Dynamics",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1139--1168",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003423",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003423",
  abstract =     "The goal of this paper is to generalize the main
                 results of [21] and subsequent papers on metric with
                 dependent quantities to the set-up of systems of linear
                 forms. In particular, we establish ``joint strong
                 extremality'' of arbitrary finite collection of smooth
                 non-degenerate submanifolds of {\mathbb{R}}$^n$. The
                 proofs are based on generalized quantitative
                 non-divergence estimates for translates of measures on
                 the space of lattices.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hoelscher:2010:RCG,
  author =       "Jing Long Hoelscher",
  title =        "Ray Class Groups of Quadratic and Cyclotomic Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1169--1182",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003447",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003447",
  abstract =     "This paper studies Galois extensions over real
                 quadratic number fields or cyclotomic number fields
                 ramified only at one prime. In both cases, the ray
                 class groups are computed, and they give restrictions
                 on the finite groups that can occur as such Galois
                 groups. Let be a real quadratic number field with a
                 prime P lying above p in {$ \mathbb {Q} $}. If p splits
                 in K/{$ \mathbb {Q} $} and p does not divide the big
                 class number of K, then any pro-p extension of K
                 ramified only at P is finite cyclic. If p is inert in
                 K/{$ \mathbb {Q} $}, then there exist infinite
                 extensions of K ramified only at P. Furthermore, for
                 big enough integer k, the ray class field (mod P$^{k +
                 1}$) is obtained from the ray class field (mod P$^k$)
                 by adjoining $ \zeta_{p^{k + 1}}$. In the case of a
                 regular cyclotomic number field $ K = \mathbb
                 {Q}(\zeta_p)$, the explicit structure of ray class
                 groups $ (m o d P^k)$ is given for any positive integer
                 $k$, where $P$ is the unique prime in $K$ above $p$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ulas:2010:VHT,
  author =       "Maciej Ulas",
  title =        "Variations on Higher Twists of Pairs of Elliptic
                 Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1183--1189",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003472",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003472",
  abstract =     "In this note we show that for any pair of elliptic
                 curves E$_1$, E$_2$ over {$ \mathbb {Q}$} with
                 j-invariant equal to 0, we can find a polynomial D \in
                 {\mathbb{Z}}[u, v, w, t] such that the sextic twists of
                 the curves E$_1$, E$_2$ by D(u, v, w, t) have rank \geq
                 2 over the field {$ \mathbb {Q}$}(u, v, w, t). A
                 similar result is proved for simultaneous quartic
                 twists of pairs of elliptic curves with j-invariant
                 1728.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Villa-Salvador:2010:EPC,
  author =       "Gabriel Villa-Salvador",
  title =        "An Elementary Proof of the Conductor--Discriminant
                 Formula",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "5",
  pages =        "1191--1197",
  month =        aug,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003459",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003459",
  abstract =     "For a finite abelian extension K/{$ \mathbb {Q} $},
                 the conductor-discriminant formula establishes that the
                 absolute value of the discriminant of K is equal to the
                 product of the conductors of the elements of the group
                 of Dirichlet characters associated to K. The simplest
                 proof uses the functional equation for the Dedekind
                 zeta function of K and its expression as the product of
                 the $L$-series attached to the various Dirichlet
                 characters associated to K. In this paper, we present
                 an elementary proof of this formula considering first K
                 contained in a cyclotomic number field of p$^n$-roots
                 of unity, where p is a prime number, and in the general
                 case, using the ramification index of p given by the
                 group of Dirichlet characters.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baczkowski:2010:V,
  author =       "Daniel Baczkowski and Michael Filaseta and Florian
                 Luca and Ognian Trifonov",
  title =        "On values of $ d(n!) / m! $, $ \varphi (n!) / m! $ and
                 $ \sigma (n!) / m! $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1199--1214",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110003435",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003435",
  abstract =     "For f one of the classical arithmetic functions d,
                 \varphi and \sigma, we establish constraints on the
                 quadruples (n, m, a, b) of integers satisfying f(n!)/m!
                 = a/b. In particular, our results imply that as nm
                 tends to infinity, the number of distinct prime
                 divisors dividing the product of the numerator and
                 denominator of the fraction f(n!)/m!, when reduced,
                 tends to infinity.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kable:2010:AIO,
  author =       "Anthony C. Kable",
  title =        "An Arithmetical Invariant of Orbits of Affine Actions
                 and Its Application to Similarity Classes of Quadratic
                 Spaces",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1215--1253",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003460",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003460",
  abstract =     "Given an action of an affine algebraic group on an
                 affine variety and a relatively invariant regular
                 function, all defined over the ring of integers of a
                 number field and having suitable additional properties,
                 an invariant of the rational orbits of the action is
                 defined. This invariant, the reduced replete Steinitz
                 class, takes its values in the reduced replete class
                 group of the number field. The general framework is
                 then applied to obtain an invariant of similarity
                 classes of non-degenerate quadratic spaces of even
                 rank. The invariant is related to more familiar
                 invariants. It is shown that if the similarity classes
                 are weighted by the volume of an associated
                 automorphism group then their reduced replete Steinitz
                 classes are asymptotically uniformly distributed with
                 respect to a natural parameter.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kohnen:2010:SNF,
  author =       "Winfried Kohnen",
  title =        "A Short Note on {Fourier} Coefficients of
                 Half-Integral Weight Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1255--1259",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003484",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003484",
  abstract =     "We give an unconditional proof of a result on sign
                 changes of Fourier coefficients of cusp forms of
                 half-integral weight that before was proved only under
                 the hypothesis of Chowla's conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vaserstein:2010:PPP,
  author =       "Leonid Vaserstein and Takis Sakkalis and Sophie
                 Frisch",
  title =        "Polynomial Parametrization of {Pythagorean} Tuples",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1261--1272",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003496",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003496",
  abstract =     "A Pythagorean (k, l)-tuple over a commutative ring A
                 is a vector x = (x$_i$) \in A$^{k + l}$, where k, l \in
                 \mathbb{N}, k \geq l which satisfies. In this paper, a
                 polynomial parametrization of Pythagorean (k, l)-tuples
                 over the ring F[t] is given, for l \geq 2. In the case
                 where l = 1, solutions of the above equation are
                 provided for k = 2, 3, 4, 5, and 9.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mammo:2010:DDA,
  author =       "Behailu Mammo",
  title =        "On the Density of Discriminants of {Abelian}
                 Extensions of a Number Field",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1273--1291",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003502",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003502",
  abstract =     "Let G = C$_{\ell }$ $ \times $ C$_{\ell }$ denote the
                 product of two cyclic groups of prime order \ell, and
                 let k be an algebraic number field. Let N(k, G, m)
                 denote the number of abelian extensions K of k with
                 Galois group G(K/k) isomorphic to G, and the relative
                 discriminant {$ \mathcal {D} $}(K/k) of norm equal to
                 m. In this paper, we derive an asymptotic formula for $
                 \sum_{m \leq X}$ N(k, G; m). This extends the result
                 previously obtained by Datskovsky and Mammo.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lozano-Robledo:2010:BTE,
  author =       "{\'A}lvaro Lozano-Robledo and Benjamin Lundell",
  title =        "Bounds for the Torsion of Elliptic Curves Over
                 Extensions with Bounded Ramification",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1293--1309",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003514",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003514",
  abstract =     "Let E be a semi-stable elliptic curve defined over {$
                 \mathbb {Q} $}, and fix N \geq 2. Let $ K_N $ /{$
                 \mathbb {Q} $} be a maximal algebraic Galois extension
                 of {$ \mathbb {Q} $} whose ramification indices are all
                 at most N. We show that there exists a computable bound
                 B(N), which depends only on N and not on the choice of
                 E/{$ \mathbb {Q} $}, such that the size of
                 E(K$_N$)$_{Tors}$ is always at most B(N).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jahangiri:2010:GAQ,
  author =       "Majid Jahangiri",
  title =        "Generators of Arithmetic Quaternion Groups and a
                 {Diophantine} Problem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1311--1328",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003551",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003551",
  abstract =     "Let p be a prime and a a quadratic non-residue (mod
                 p). Then the set of integral solutions of the
                 Diophantine equation form a cocompact discrete subgroup
                 \Gamma$_{p, a}$ \subset SL(2, {\mathbb{R}}) which is
                 commensurable with the group of units of an order in a
                 quaternion algebra over {$ \mathbb {Q}$}. The problem
                 addressed in this paper is an estimate for the traces
                 of a set of generators for \Gamma$_{p, a}$. Empirical
                 results summarized in several tables show that the
                 trace has significant and irregular fluctuations which
                 is reminiscent of the behavior of the size of a
                 generator for the solutions of Pell's equation. The
                 geometry and arithmetic of the group of units of an
                 order in a quaternion algebra play a key role in the
                 development of the code for the purpose of this
                 paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Tanti:2010:ECS,
  author =       "Jagmohan Tanti and S. A. Katre",
  title =        "{Euler}'s Criterion for Septic Nonresidues",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1329--1347",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003563",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003563",
  abstract =     "Let p be a prime \equiv 1 (mod 7). In this paper, we
                 obtain an explicit expression for a primitive seventh
                 root of unity (mod p) in terms of coefficients of a
                 Jacobi sum of order 7 and also in terms of a solution
                 of a Diophantine system of Leonard and Williams, and
                 then obtain Euler's criterion for septic nonresidues D
                 (mod p) in terms of this seventh root. Explicit results
                 are given for septic nonresidues for D = 2, 3, 5, 7.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Booher:2010:ECT,
  author =       "Jeremy Booher and Anastassia Etropolski and Amanda
                 Hittson",
  title =        "Evaluations of Cubic Twisted {Kloosterman} Sheaf
                 Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1349--1365",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003538",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003538",
  abstract =     "We prove some conjectures of Evans and Katz presented
                 in a paper by Evans regarding twisted Kloosterman sheaf
                 sums T$_n$. These conjectures give explicit evaluations
                 of the sums T$_n$ where the character is cubic and n =
                 4. There are also conjectured relationships between
                 evaluations of T$_n$ and the coefficients of certain
                 modular forms. For three of these modular forms, each
                 of weight 3, it is conjectured that the coefficients
                 are related to the squares of the coefficients of
                 weight 2 modular forms. We prove these relationships
                 using the theory of complex multiplication.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Verrill:2010:CRM,
  author =       "H. A. Verrill",
  title =        "Congruences Related to Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1367--1390",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003587",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003587",
  abstract =     "Let $f$ be a modular form of weight $k$ for a
                 congruence subgroup $ \Gamma \subset \mathrm {SL}_2
                 (Z)$, and $t$ a weight $0$ modular function for $
                 \Gamma $. Assume that near $ t = 0$, we can write $ f =
                 \sum_{n \geq 0} b_n t^n$, $ b_n \in Z$. Let $ \ell (z)$
                 be a weight $ k + 2$ modular form with $q$-expansion $
                 \sum \gamma_n q^n$, such that the Mellin transform of $
                 \ell $ can be expressed as an Euler product. Then we
                 show that if for some integers $ a_i$, $ d_i$, then the
                 congruence relation $ b_{mp^r} - \gamma_p b_{mp^{r -
                 1}} + \varepsilon_p p^{k + 1} b_{mp^{r - 2}} \equiv 0
                 (\bmod p^r)$ holds. We give a number of examples of
                 this phenomena.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{David:2010:SFD,
  author =       "Chantal David and Jorge Jim{\'e}nez Urroz",
  title =        "Square-Free Discriminants of {Frobenius} Rings",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1391--1412",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003599",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003599",
  abstract =     "Let E be an elliptic curve over {$ \mathbb {Q} $}. We
                 know that the ring of endomorphisms of its reduction
                 modulo an ordinary prime p is an order of the quadratic
                 imaginary field generated by the Frobenius element
                 \pi$_p$. However, except in the trivial case of complex
                 multiplication, very little is known about the fields
                 that appear as algebras of endomorphisms when p varies.
                 In this paper, we study the endomorphism ring by
                 looking at the arithmetic of, the discriminant of the
                 characteristic polynomial of \pi$_p$. In particular, we
                 give a precise asymptotic for the function counting the
                 number of primes p up to x such that is square-free and
                 in certain congruence class fixed {\em a priori\/},
                 when averaging over elliptic curves defined over the
                 rationals. We discuss the relation of this result with
                 the Lang--Trotter conjecture, and some other questions
                 on the curve modulo p.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hambleton:2010:QRR,
  author =       "S. Hambleton and V. Scharaschkin",
  title =        "Quadratic Reciprocity Via Resultants",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1413--1417",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000354X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000354X",
  abstract =     "We give a simple inductive proof of quadratic
                 reciprocity using resultants.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lebacque:2010:TVI,
  author =       "Philippe Lebacque",
  title =        "On {Tsfasman--Vl{\u{a}}du{\c{t}}} invariants of
                 infinite global fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "6",
  pages =        "1419--1448",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003526",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003526",
  abstract =     "In this paper, we study certain asymptotic properties
                 of global fields. We consider the set of
                 Tsfasman--Vl{\u{a}}du{\c{t}} invariants of infinite
                 global fields and answer some natural questions arising
                 from their work. In particular, we prove the existence
                 of infinite global fields having finitely many strictly
                 positive invariants at given places, and the existence
                 of infinite number fields with certain prescribed
                 invariants being zero. We also give precisions on the
                 deficiency of infinite global fields and on the primes
                 decomposition in those fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dujella:2010:SSP,
  author =       "Andrej Dujella and Ana Jurasi{\'c}",
  title =        "On the Size of Sets in a Polynomial Variant of a
                 Problem of {Diophantus}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1449--1471",
  month =        nov,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110003575",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003575",
  abstract =     "In this paper, we prove that there does not exist a
                 set of 8 polynomials (not all constant) with
                 coefficients in an algebraically closed field of
                 characteristic 0 with the property that the product of
                 any two of its distinct elements plus 1 is a perfect
                 square.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ehlen:2010:TBP,
  author =       "Stephan Ehlen",
  title =        "Twisted {Borcherds} Products on {Hilbert} Modular
                 Surfaces and the Regularized Theta Lift",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1473--1489",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003642",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003642",
  abstract =     "We construct a lifting from weakly holomorphic modular
                 forms of weight 0 for SL$_2$ ({\mathbb{Z}}) with
                 integral Fourier coefficients to meromorphic Hilbert
                 modular forms of weight 0 for the full Hilbert modular
                 group of a real quadratic number field with an infinite
                 product expansion and a divisor given by a linear
                 combination of twisted Hirzebruch--Zagier divisors. The
                 construction uses the singular theta lifting by
                 considering a suitable twist of a Siegel theta
                 function. We generalize the work by Bruinier and Yang
                 who showed the existence of the lifting for prime
                 discriminants using a different approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Belabas:2010:DCP,
  author =       "Karim Belabas and {\'E}tienne Fouvry",
  title =        "Discriminants cubiques et progressions
                 arithm{\'e}tiques. ({French}) [{Cubic} discriminants
                 and arithmetic progressions]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1491--1529",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003605",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003605",
  abstract =     "Nous calculons la densit{\'e} des discriminants des
                 corps sextiques galoisiens de groupe S$_3$,
                 d{\'e}montrant un nouveau cas de la conjecture de Malle
                 ainsi qu'un cas particulier de sa
                 g{\'e}n{\'e}ralisation par Ellenberg et Venkatesh. Plus
                 g{\'e}n{\'e}ralement, nous {\'e}tudions la densit{\'e}
                 des discriminants de corps cubiques dans une
                 progression arithm{\'e}tique, avec une zone
                 d'uniformit{\'e} la plus large possible. We compute the
                 density of discriminants of Galois sextic fields with
                 group S$_3$, thereby proving a new case of Malle's
                 conjecture as well as a special case of its
                 generalization by Ellenberg and Venkatesh. Further, we
                 study the density of cubic discriminants in an
                 arithmetic progression, in the largest possible
                 uniformity with respect to the modulus.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Patkowski:2010:CGF,
  author =       "Alexander E. Patkowski",
  title =        "On Curious Generating Functions for Values of
                 {$L$}-Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1531--1540",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003630",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003630",
  abstract =     "We prove some curious identities for generating
                 functions for values of {$L$}-functions. It is shown
                 how to obtain generating functions for values of
                 {$L$}-functions using a slightly different approach,
                 resulting in some new $q$-series identities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Wu:2010:RGD,
  author =       "Qingquan Wu and Renate Scheidler",
  title =        "The Ramification Groups and Different of a Compositum
                 of {Artin--Schreier} Extensions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1541--1564",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003617",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003617",
  abstract =     "Let K be a function field over a perfect constant
                 field of positive characteristic p, and L the
                 compositum of n (degree p) Artin--Schreier extensions
                 of K. Then much of the behavior of the degree p$^n$
                 extension L/K is determined by the behavior of the
                 degree p intermediate extensions M/K. For example, we
                 prove that a place of K totally ramifies/is
                 inert/splits completely in L if and only if it totally
                 ramifies/is inert/splits completely in every M.
                 Examples are provided to show that all possible
                 decompositions are in fact possible; in particular, a
                 place can be inert in a non-cyclic Galois function
                 field extension, which is impossible in the case of a
                 number field. Moreover, we give an explicit closed form
                 description of all the different exponents in L/K in
                 terms of those in all the M/K. Results of a similar
                 nature are given for the genus, the regulator, the
                 ideal class number and the divisor class number. In
                 addition, for the case n = 2, we provide an explicit
                 description of the ramification group filtration of
                 L/K.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pickett:2010:CSD,
  author =       "Erik Jarl Pickett",
  title =        "Construction of Self-Dual Integral Normal Bases in
                 {Abelian} Extensions of Finite and Local Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1565--1588",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003654",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003654",
  abstract =     "Let F/E be a finite Galois extension of fields with
                 abelian Galois group \Gamma. A self-dual normal basis
                 for F/E is a normal basis with the additional property
                 that Tr$_{F / E}$ (g(x), h(x)) = \delta$_{g, h}$ for g,
                 h \in \Gamma. Bayer-Fluckiger and Lenstra have shown
                 that when char(E) \neq 2, then F admits a self-dual
                 normal basis if and only if [F : E] is odd. If F/E is
                 an extension of finite fields and char(E) = 2, then F
                 admits a self-dual normal basis if and only if the
                 exponent of \Gamma is not divisible by 4. In this
                 paper, we construct self-dual normal basis generators
                 for finite extensions of finite fields whenever they
                 exist. Now let K be a finite extension of {$ \mathbb
                 {Q}$}$_p$, let L/K be a finite abelian Galois extension
                 of odd degree and let be the valuation ring of L. We
                 define A$_{L / K}$ to be the unique fractional -ideal
                 with square equal to the inverse different of L/K. It
                 is known that a self-dual integral normal basis exists
                 for A$_{L / K}$ if and only if L/K is weakly ramified.
                 Assuming p \neq 2, we construct such bases whenever
                 they exist.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Robertson:2010:MCF,
  author =       "Leanne Robertson",
  title =        "Monogeneity in Cyclotomic Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1589--1607",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003666",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003666",
  abstract =     "A number field is said to be {\em monogenic\/} if its
                 ring of integers is a simple ring extension
                 {\mathbb{Z}}[\alpha ] of {\mathbb{Z}}. It is a
                 classical and usually difficult problem to determine
                 whether a given number field is monogenic and, if it
                 is, to find all numbers \alpha that generate a power
                 integral basis {1, \alpha, \alpha$^2$, \ldots,
                 \alpha$^k$ } for the ring. The nth cyclotomic field {$
                 \mathbb {Q}$}(\zeta$_n$) is known to be monogenic for
                 all n, and recently Ranieri proved that if n is coprime
                 to 6, then up to integer translation all the integral
                 generators for {$ \mathbb {Q}$}(\zeta$_n$) lie on the
                 unit circle or the line Re(z) = 1/2 in the complex
                 plane. We prove that this geometric restriction extends
                 to the cases n = 3k and n = 4k, where k is coprime to
                 6. We use this result to find all power integral bases
                 for {$ \mathbb {Q}$}(\zeta$_n$) for n = 15, 20, 21, 28.
                 This leads us to a conjectural solution to the problem
                 of finding all integral generators for cyclotomic
                 fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Feigon:2010:EAC,
  author =       "Brooke Feigon and David Whitehouse",
  title =        "Exact Averages of Central Values of Triple Product
                 {$L$}-Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1609--1624",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000368X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000368X",
  abstract =     "We obtain exact formulas for central values of triple
                 product {$L$}-functions averaged over newforms of
                 weight 2 and prime level. We apply these formulas to
                 non-vanishing problems. This paper uses a period
                 formula for the triple product {$L$}-function proved by
                 Gross and Kudla.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Katayama:2010:GGF,
  author =       "Koji Katayama",
  title =        "Generalized Gamma Functions with Characters",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1625--1657",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003629",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003629",
  abstract =     "The main objective of this paper is to define \Gamma
                 functions \Gamma [\chi ](v) with characters \chi and
                 study their properties. To this end, we ought to
                 introduce {$L$}-functions of Hurwitz type. We prove
                 that holds, which combines the theory at ``s = 0'' and
                 the theory at ``s = 1''.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bostan:2010:GFC,
  author =       "Alin Bostan and Bruno Salvy and Khang Tran",
  title =        "Generating Functions of {Chebyshev}-Like Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1659--1667",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003691",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003691",
  abstract =     "In this short note, we give simple proofs of several
                 results and conjectures formulated by Stolarsky and
                 Tran concerning generating functions of some families
                 of Chebyshev-like polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lee:2010:SPF,
  author =       "K. S. Enoch Lee",
  title =        "On the Sum of a Prime and a {Fibonacci} Number",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1669--1676",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003708",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003708",
  abstract =     "We show that the set of the numbers that are the sum
                 of a prime and a Fibonacci number has positive lower
                 asymptotic density.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dewar:2010:RCS,
  author =       "Michael Dewar and Olav K. Richter",
  title =        "{Ramanujan} Congruences for {Siegel} Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1677--1687",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000371X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000371X",
  abstract =     "We determine conditions for the existence and
                 non-existence of Ramanujan-type congruences for Jacobi
                 forms. We extend these results to Siegel modular forms
                 of degree 2 and as an application, we establish
                 Ramanujan-type congruences for explicit examples of
                 Siegel modular forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Schwab:2010:GAF,
  author =       "Emil Daniel Schwab",
  title =        "Generalized Arithmetical Functions of Three
                 Variables",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1689--1699",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003721",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003721",
  abstract =     "The paper is devoted to the study of some properties
                 of generalized arithmetical functions extended to the
                 case of three variables. The convolution in this case
                 is a convolution of the incidence algebra of a
                 M{\"o}bius category in the sense of Leroux. This
                 category is a two-sided analogue of the poset (it is
                 viewed as a category) of positive integers ordered by
                 divisibility.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sairaiji:2010:FGJ,
  author =       "Fumio Sairaiji",
  title =        "Formal Groups of {Jacobian} Varieties of Hyperelliptic
                 Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "7",
  pages =        "1701--1716",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003733",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:23 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003733",
  abstract =     "Let k be a field of characteristic zero. In this
                 paper, we discuss two explicit constructions of the
                 formal groups {\u{0}134} of the Jacobian varieties J of
                 hyperelliptic curves C over k. Our results are
                 generalizations of the classical constructions of
                 formal groups of elliptic curves. As an application of
                 our results, we may decide the type of bad reduction of
                 J modulo p when C is a hyperelliptic curve over {$
                 \mathbb {Q} $}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Templier:2010:AVC,
  author =       "Nicolas Templier",
  title =        "On Asymptotic Values of Canonical Quadratic
                 {$L$}-Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1717--1730",
  month =        dec,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042110003678",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003678",
  abstract =     "We establish an asymptotic for the first moment of
                 Hecke $L$-series associated to canonical characters on
                 imaginary quadratic fields. This provides another proof
                 and improves recent results by Masri and
                 Kim--Masri--Yang.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Samuels:2010:FCU,
  author =       "Charles L. Samuels",
  title =        "The Finiteness of Computing the Ultrametric {Mahler}
                 Measure",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1731--1753",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003745",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003745",
  abstract =     "Recent work of Fili and the author examines an
                 ultrametric version of the Mahler measure, denoted
                 M$_{\infty }$ (\alpha) for an algebraic number \alpha.
                 We show that the computation of M$_{\infty }$ (\alpha)
                 can be reduced to a certain search through a finite
                 set. Although it is an open problem to record the
                 points of this set in general, we provide some examples
                 where it is reasonable to compute and our result can be
                 used to determine M$_{\infty }$ (\alpha).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kang:2010:APT,
  author =       "Soon-Yi Kang and Chang Heon Kim",
  title =        "Arithmetic Properties of Traces of Singular Moduli on
                 Congruence Subgroups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1755--1768",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003757",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003757",
  abstract =     "After Zagier proved that the traces of singular moduli
                 are Fourier coefficients of a weakly holomorphic
                 modular form, various arithmetic properties of the
                 traces of singular values of modular functions mostly
                 on the full modular group have been found. The purpose
                 of this paper is to generalize the results for modular
                 functions on congruence subgroups with arbitrary
                 level.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sbeity:2010:CSE,
  author =       "Farah Sbeity and Boucha{\"i}b Soda{\"i}gui",
  title =        "Classes de {Steinitz} d'extensions non ab{\'e}liennes
                 {\`a} groupe de {Galois} d'ordre $1$6 ou
                 extrasp{\'e}cial d'ordre $ 32$ et probl{\`e}me de
                 plongement. ({French}) [{Steinitz} classes of
                 non-Abelian extensions to {Galois} group of order $ 16
                 $ or extraspecial of order $ 32$ and embedding
                 problem]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1769--1783",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003794",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003794",
  abstract =     "Soient k un corps de nombres et Cl(k) son groupe des
                 classes. Soit \Gamma un groupe non ab{\'e}lien d'ordre
                 16, ou un groupe extrasp{\'e}cial d'ordre 32. Soit
                 R$_m$ (k, \Gamma) le sous-ensemble de Cl(k) form{\'e}
                 par les {\'e}l{\'e}ments qui sont r{\'e}alisables par
                 les classes de Steinitz d'extensions galoisiennes de k,
                 mod{\'e}r{\'e}ment ramifi{\'e}es et dont le groupe de
                 Galois est isomorphe {\`a} \Gamma. Lorsque \Gamma est
                 le groupe modulaire d'ordre 16, on suppose que k
                 contienne une racine primitive 4{\`e}me de l'unit{\'e}.
                 Dans cet article on montre que R$_m$ (k, \Gamma) est le
                 groupe Cl(k) tout entier si le nombre des classes de k
                 est impair. On {\'e}tudie un probl{\`e}me de plongement
                 en liaison avec les classes de Steinitz dans la
                 perspective de l'{\'e}tude des classes galoisiennes
                 r{\'e}alisables. On prouve que pour tout c \in Cl(k),
                 il existe une extension quadratique de k,
                 mod{\'e}r{\'e}e, dont la classe de Steinitz est c, et
                 qui est plongeable dans une extension galoisienne de k,
                 mod{\'e}r{\'e}e et {\`a} groupe de Galois isomorphe
                 {\`a} \Gamma. Let k be a number field and Cl(k) its
                 class group. Let \Gamma be a nonabelian group of order
                 16 or an extra-special group of order 32. Let R$_m$ (k,
                 \Gamma) be the subset of Cl(k) consisting of those
                 classes which are realizable as Steinitz classes of
                 tame Galois extensions of k with Galois group
                 isomorphic to \Gamma. When \Gamma is the modular group
                 of order 16, we assume that k contains a primitive 4th
                 root of unity. In the present paper, we show that R$_m$
                 (k, \Gamma) is the full group Cl(k) if the class number
                 of k is odd. We study an embedding problem connected
                 with Steinitz classes in the perspective of studying
                 realizable Galois module classes. We prove that for all
                 c \in Cl(k), there exist a tame quadratic extension of
                 k, with Steinitz class c, and which is embeddable in a
                 tame Galois extension of k with Galois group isomorphic
                 to \Gamma.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Lucht:2010:SRE,
  author =       "Lutz G. Lucht",
  title =        "A Survey of {Ramanujan} Expansions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1785--1799",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003800",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003800",
  abstract =     "This paper summarizes the development of Ramanujan
                 expansions of arithmetic functions since Ramanujan's
                 paper in 1918, following Carmichael's mean-value-based
                 concept from 1932 up to 1994. A new technique, based on
                 the concept of related arithmetic functions, is
                 introduced that leads to considerable extensions of
                 preceding results on Ramanujan expansions. In
                 particular, very short proofs of theorems for additive
                 and multiplicative functions going far beyond previous
                 borders are presented, and Ramanujan expansions that
                 formerly have been considered mysterious are
                 explained.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cai:2010:LFS,
  author =       "Yingchun Cai",
  title =        "{Lagrange}'s Four Squares Theorem with Variables of
                 Special Type",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1801--1817",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003812",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003812",
  abstract =     "Let N denote a sufficiently large integer satisfying N
                 \equiv 4 (mod 24), and P$_r$ denote an almost-prime
                 with at most r prime factors, counted according to
                 multiplicity. In this paper, we proved that the
                 equation is solvable in one prime and three P$_{42}$,
                 or in four P$_{13}$. These results constitute
                 improvements upon that of Heath-Brown and Tolev.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Barman:2010:IIT,
  author =       "Rupam Barman and Anupam Saikia",
  title =        "{Iwasawa} $ \lambda $-invariants and {$ \Gamma
                 $}-transforms of $p$-adic measures on {$ \mathbb
                 {Z}_p^n $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1819--1829",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003824",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003824",
  abstract =     "In this paper, we determine a relation between the
                 \lambda -invariants of a $p$-adic measure on and its
                 \Gamma transform. Along the way we also determine
                 $p$-adic properties of certain Mahler coefficients.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Caranay:2010:ESP,
  author =       "Perlas C. Caranay and Renate Scheidler",
  title =        "An Efficient Seventh Power Residue Symbol Algorithm",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1831--1853",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003770",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003770",
  abstract =     "Power residue symbols and their reciprocity laws have
                 applications not only in number theory, but also in
                 other fields like cryptography. A crucial ingredient in
                 certain public key cryptosystems is a fast algorithm
                 for computing power residue symbols. Such algorithms
                 have only been devised for the Jacobi symbol as well as
                 for cubic and quintic power residue symbols, but for no
                 higher powers. In this paper, we provide an efficient
                 procedure for computing 7th power residue symbols. The
                 method employs arithmetic in the field {$ \mathbb {Q}
                 $}(\zeta), with \zeta a primitive 7th root of unity,
                 and its ring of integers {\mathbb{Z}}[\zeta ]. We give
                 an explicit characterization for an element in
                 {\mathbb{Z}}[\zeta ] to be primary, and provide an
                 algorithm for finding primary associates of integers in
                 {\mathbb{Z}}[\zeta ]. Moreover, we formulate explicit
                 forms of the complementary laws to Kummer's 7th degree
                 reciprocity law, and use Lenstra's norm-Euclidean
                 algorithm in the cyclotomic field.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{DelCorso:2010:NII,
  author =       "Ilaria {Del Corso} and Roberto Dvornicich",
  title =        "Non-Invariance of the Index in Wildly Ramified
                 Extensions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1855--1868",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003836",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003836",
  abstract =     "In this paper, we give an example of three wildly
                 ramified extensions L$_1$, L$_2$, L$_3$ of {$ \mathbb
                 {Q}$}$_2$ with the same ramification numbers and
                 isomorphic Galois groups, such that I(nL$_1$ ) >
                 I(nL$_2$) > I(nL$_3$) for a suitable integer n (where
                 I(nL) denotes the index of the {$ \mathbb
                 {Q}$}$_2$-algebra L$^n$). This example shows that the
                 condition given in [2] for the invariance of the index
                 of tamely ramified extensions is no longer sufficient
                 in the general case.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Laishram:2010:CRP,
  author =       "Shanta Laishram",
  title =        "On a Conjecture on {Ramanujan} Primes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1869--1873",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003848",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003848",
  abstract =     "For n \geq 1, the {\em nth Ramanujan prime\/} is
                 defined to be the smallest positive integer R$_n$ with
                 the property that if x \geq R$_n$, then where \pi (\nu)
                 is the number of primes not exceeding \nu for any \nu >
                 0 and \nu \in {\mathbb{R}}. In this paper, we prove a
                 conjecture of Sondow on upper bound for Ramanujan
                 primes. An explicit bound of Ramanujan primes is also
                 given. The proof uses explicit bounds of prime \pi and
                 \theta functions due to Dusart.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vienney:2010:NCA,
  author =       "Mathieu Vienney",
  title =        "A new construction of $p$-adic {Rankin} convolutions
                 in the case of positive slope",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1875--1900",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003782",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003782",
  abstract =     "Given two newforms f and g of respective weights k and
                 l with l < k, Hida constructed a $p$-adic
                 {$L$}-function interpolating the values of the Rankin
                 convolution of f and g in the critical strip l \leq s
                 \leq k. However, this construction works only if f is
                 an ordinary form. Using a method developed by
                 Panchishkin to construct $p$-adic {$L$}-function
                 associated with modular forms, we generalize this
                 construction to the case where the slope of f is
                 small.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Brown:2010:SVF,
  author =       "Jim Brown",
  title =        "Special values of {$L$}-functions on {$ \mathrm
                 {GSp}_4 \times \mathrm {GL}_2$} and the non-vanishing
                 of {Selmer} groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1901--1926",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003769",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003769",
  abstract =     "In this paper, we show how one can use an inner
                 product formula of Heim giving the inner product of the
                 pullback of an Eisenstein series from Sp$_{10}$ to
                 Sp$_2$ $ \times $ Sp$_4$ $ \times $ Sp$_4$ with a
                 new-form on GL$_2$ and a Saito--Kurokawa lift to
                 produce congruences between Saito--Kurokawa lifts and
                 non-CAP forms. This congruence is in part controlled by
                 the {$L$}-function on GSp$_4$ $ \times $ GL$_2$. The
                 congruence is then used to produce nontrivial torsion
                 elements in an appropriate Selmer group, providing
                 evidence for the Bloch--Kato conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kaneko:2010:KDM,
  author =       "Masanobu Kaneko and Yasuo Ohno",
  title =        "On a Kind of Duality of Multiple Zeta-Star Values",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1927--1932",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S179304211000385X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211000385X",
  abstract =     "A duality-type relation for height one multiple
                 zeta-star values is established. A conjectural
                 generalization to the case of arbitrary height is also
                 presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bettin:2010:SMR,
  author =       "Sandro Bettin",
  title =        "The Second Moment of the {Riemann} Zeta Function with
                 Unbounded Shifts",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1933--1944",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003861",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003861",
  abstract =     "We prove an asymptotic formula for the second moment
                 (up to height T) of the Riemann zeta function with two
                 shifts. The case we deal with is where the real parts
                 of the shifts are very close to zero and the imaginary
                 parts can grow up to T$^{2 - \varepsilon }$, for any
                 \varepsilon > 0.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2010:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 6)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "8",
  pages =        "1945--1950",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003885",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042110003885",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Joshi:2011:IHC,
  author =       "Kirti Joshi and Cameron Mcleman",
  title =        "Infinite {Hilbert} Class Field Towers from {Galois}
                 Representations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "1--8",
  month =        feb,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111003879",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003879",
  abstract =     "We investigate class field towers of number fields
                 obtained as fixed fields of modular representations of
                 the absolute Galois group of the rational numbers.
                 First, for each k \in {12, 16, 18, 20, 22, 26}, we give
                 explicit rational primes \ell such that the fixed field
                 of the mod-\ell representation attached to the unique
                 normalized cusp eigenform of weight k on SL$_2$
                 ({\mathbb{Z}}) has an infinite class field tower.
                 Further, under a conjecture of Hardy and Littlewood, we
                 prove the existence of infinitely many cyclotomic
                 fields of prime conductor, providing infinitely many
                 such primes \ell for each k in the list. Finally, given
                 a non-CM curve E/{$ \mathbb {Q}$}, we show that there
                 exists an integer M$_E$ such that the fixed field of
                 the representation attached to the n-division points of
                 E has an infinite class field tower for a set of
                 integers n of density one among integers coprime to
                 M$_E$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nguyen:2011:CDM,
  author =       "Lan Nguyen",
  title =        "A Complete Description of Maximal Solutions of
                 Functional Equations Arising from Multiplication of
                 Quantum Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "9--56",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003909",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003909",
  abstract =     "In this paper, we resolve a problem raised by
                 Nathanson concerning the maximal solutions to
                 functional equations naturally arising from
                 multiplication of quantum integers ([4]). Together with
                 our results obtained in [11], which treats the case
                 where the field of coefficients is {$ \mathbb {Q} $},
                 this provides a complete description of the maximal
                 solutions to these functional equations and their
                 support bases P in characteristic zero setting.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Heuberger:2011:PDA,
  author =       "Clemens Heuberger and Helmut Prodinger",
  title =        "A precise description of the $p$-adic valuation of the
                 number of alternating sign matrices",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "57--69",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003892",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003892",
  abstract =     "Following Sun and Moll ([4]), we study v$_p$ (T(N)),
                 the $p$-adic valuation of the counting function of the
                 alternating sign matrices. We find an exact analytic
                 expression for it that exhibits the fluctuating
                 behavior, by means of Fourier coefficients. The method
                 is the Mellin--Perron technique, which is familiar in
                 the analysis of the sum-of-digits function and related
                 quantities.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zhang:2011:FPM,
  author =       "Deyu Zhang and Wenguang Zhai",
  title =        "On the fifth-power moment of {$ \Delta (x) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "71--86",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003922",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003922",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Buckingham:2011:FGI,
  author =       "Paul Buckingham",
  title =        "The Fractional {Galois} Ideal for Arbitrary Order of
                 Vanishing",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "87--99",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004010",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004010",
  abstract =     "We propose a candidate, which we call the fractional
                 Galois ideal after Snaith's fractional ideal, for
                 replacing the classical Stickelberger ideal associated
                 to an abelian extension of number fields. The
                 Stickelberger ideal can be seen as gathering
                 information about those {$L$}-functions of the
                 extension which are non-zero at the special point s =
                 0, and was conjectured by Brumer to give annihilators
                 of class-groups viewed as Galois modules. An earlier
                 version of the fractional Galois ideal extended the
                 Stickelberger ideal to include {$L$}-functions with a
                 simple zero at s = 0, and was shown by the present
                 author to provide class-Group annihilators not existing
                 in the Stickelberger ideal. The version presented in
                 this paper deals with {$L$}-functions of arbitrary
                 order of vanishing at s = 0, and we give evidence using
                 results of Popescu and Rubin that it is closely related
                 to the Fitting ideal of the class-group, a canonical
                 ideal of annihilators. Finally, we prove an equality
                 involving Stark elements and class-groups originally
                 due to B{\"u}y{\"u}kboduk, but under a slightly
                 different assumption, the advantage being that we need
                 none of the Kolyvagin system machinery used in the
                 original proof.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gurak:2011:GKS,
  author =       "S. Gurak",
  title =        "{Gauss} and {Kloosterman} Sums Over Residue Rings of
                 Algebraic Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "101--114",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003958",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003958",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bremner:2011:RPS,
  author =       "Andrew Bremner and Maciej Ulas",
  title =        "Rational Points on Some Hyper- and Superelliptic
                 Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "115--132",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003946",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003946",
  abstract =     "We construct families of certain hyper- and
                 superelliptic curves that contain a (small) number of
                 rational points. This leads to lower bounds for the
                 ranks of Jacobians of certain high genus curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Fu:2011:CPO,
  author =       "Shishuo Fu",
  title =        "Combinatorial Proof of One Congruence for the Broken
                 $1$-Diamond Partition and a Generalization",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "133--144",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004022",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004022",
  abstract =     "In one of their recent collaborative papers, Andrews
                 and Paule continue their study of partition functions
                 via MacMahon's Partition Analysis by considering
                 partition functions associated with directed graphs
                 which consist of chains of diamond shape. They prove a
                 congruence related to one of these partition functions
                 and conjecture a number of similar congruence results.
                 In this note, we reprove this congruence by
                 constructing an explicit way to group partitions. Then
                 we keep the essence of the method and manage to apply
                 it to a different kind of plane partitions to get more
                 general results and several other congruences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cosgrave:2011:MOC,
  author =       "John B. Cosgrave and Karl Dilcher",
  title =        "The Multiplicative Orders of Certain {Gauss}
                 Factorials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "145--171",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100396X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100396X",
  abstract =     "A theorem of Gauss extending Wilson's theorem states
                 the congruence (n - 1)$_n$ ! \equiv -1 (mod n) whenever
                 n has a primitive root, and \equiv 1 (mod n) otherwise,
                 where N$_n$ ! denotes the product of all integers up to
                 N that are relatively prime to n. In the spirit of this
                 theorem, we study the multiplicative orders of (mod n)
                 for odd prime powers p$^{\alpha }$. We prove a general
                 result about the connection between the order for
                 p$^{\alpha }$ and for p$^{\alpha + 1}$ and study
                 exceptions to the general rule. Particular emphasis is
                 given to the cases M = 3, M = 4 and M = 6, while the
                 case M = 2 is already known.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Carls:2011:GTC,
  author =       "Robert Carls",
  title =        "{Galois} Theory of the Canonical Theta Structure",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "173--202",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003934",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003934",
  abstract =     "In this article, we give a Galois-theoretic
                 characterization of the canonical theta structure. The
                 Galois property of the canonical theta structure
                 translates into certain $p$-adic theta relations which
                 are satisfied by the canonical theta null point of the
                 canonical lift. As an application, we prove some 2-adic
                 theta identities which describe the set of canonical
                 theta null points of the canonical lifts of ordinary
                 abelian varieties in characteristic 2. The latter theta
                 relations are suitable for explicit canonical lifting.
                 Using the theory of canonical theta null points, we are
                 able to give a theoretical foundation to Mestre's point
                 counting algorithm which is based on the computation of
                 the generalized arithmetic geometric mean sequence.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hubrechts:2011:MEH,
  author =       "Hendrik Hubrechts",
  title =        "Memory Efficient Hyperelliptic Curve Point Counting",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "203--214",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004034",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004034",
  abstract =     "In recent algorithms that use deformation in order to
                 compute the number of points on varieties over a finite
                 field, certain differential equations of matrices over
                 $p$-adic fields emerge. We present a novel strategy to
                 solve this kind of equations in a memory efficient way.
                 The main application is an algorithm requiring
                 quasi-cubic time and only quadratic memory in the
                 parameter n, that solves the following problem: for E a
                 hyperelliptic curve of genus g over a finite field of
                 extension degree n and small characteristic, compute
                 its zeta function. This improves substantially upon
                 Kedlaya's result which has the same quasi-cubic time
                 asymptotic, but requires also cubic memory size.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Boulet:2011:SMD,
  author =       "Cilanne Boulet and Ka{\u{g}}an Kur{\c{s}}ung{\"o}z",
  title =        "Symmetry of $k$-marked {Durfee} symbols",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "215--230",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003971",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003971",
  abstract =     "Andrews introduced the k-marked Durfee symbols in his
                 work defining a variant of the Atkin--Garvan moments of
                 ranks. He provided and proved many identities and
                 congruences using analytical methods. Here, we give an
                 equivalent description of k-marked Durfee symbols, and
                 using it we give combinatorial proofs to two results of
                 Andrews'.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Brink:2011:RFD,
  author =       "David Brink",
  title =        "{R{\'e}dei} Fields and Dyadic Extensions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "231--240",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003983",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003983",
  abstract =     "For an arbitrary non-square discriminant D, the {\em
                 R{\'e}dei field\/} \Gamma$_0$ (D) is introduced as an
                 extension of analogous to the genus field and connected
                 with the R{\'e}dei--Reichardt Theorem. It is shown how
                 to compute R{\'e}dei fields, and this is used to find
                 socles of dyadic extensions of K for negative D.
                 Finally, a theorem and two conjectures are presented
                 relating the fields and for an odd prime p.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Li:2011:WWL,
  author =       "Xiaoqing Li",
  title =        "A Weighted {Weyl} Law for the Modular Surface",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "241--248",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111003995",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003995",
  abstract =     "In this paper, we will prove a Weyl law for the
                 modular surface weighted by the first Fourier
                 coefficient of the Maass cusp forms. Our error term
                 corresponds to the best known error term in the Weyl
                 law and improves a previous result of Kuznetsov.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baba:2011:OSM,
  author =       "Srinath Baba and H{\aa}kan Granath",
  title =        "Orthogonal Systems of Modular Forms and Supersingular
                 Polynomials",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "249--259",
  month =        feb,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004009",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:24 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004009",
  abstract =     "We extend a construction of Kaneko and Zagier to
                 obtain modular forms which, modulo a prime, vanish at
                 the supersingular points. These modular forms arise
                 simultaneously as solutions of certain second-order
                 differential equations, and as an orthogonal basis for
                 an inner product on the space of modular forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Carter:2011:BGP,
  author =       "Andrea C. Carter",
  title =        "The {Brauer} Group of {Del Pezzo} Surfaces",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "261--287",
  month =        mar,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111003910",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111003910",
  abstract =     "Let S$_1$ be a Del Pezzo surface of degree 1 over a
                 number field k. We establish a criterion for the
                 existence of a nontrivial element of order 5 in the
                 Brauer group of S$_1$ in terms of certain Galois-stable
                 configurations of exceptional divisors on this
                 surface.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Roberts:2011:NPF,
  author =       "David P. Roberts",
  title =        "Nonsolvable Polynomials with Field Discriminant {$ 5^A
                 $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "289--322",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004113",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004113",
  abstract =     "We present the first explicitly known polynomials in
                 Z[x] with nonsolvable Galois group and field
                 discriminant of the form \pm p$^A$ for p \leq 7 a
                 prime. Our main polynomial has degree 25, Galois group
                 of the form PSL$_2$ (5)$^5$. 10, and field discriminant
                 5$^{69}$. A closely related polynomial has degree 120,
                 Galois group of the form SL$_2$ (5)$^5$. 20, and field
                 discriminant 5$^{311}$. We completely describe 5-adic
                 behavior, finding in particular that the root
                 discriminant of both splitting fields is 125 \cdotp
                 5$^{-1 / 12500}$ \approx 124.984 and the class number
                 of the latter field is divisible by 5$^4$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Murty:2011:TCI,
  author =       "M. Ram Murty and Chester J. Weatherby",
  title =        "On the Transcendence of Certain Infinite Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "323--339",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004058",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004058",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Barcau:2011:CCF,
  author =       "Mugurel Barcau and Vicen{\c{t}}iu Pa{\c{s}}ol",
  title =        "$ \bmod p $ congruences for cusp forms of weight four
                 for {$ \Gamma_0 (p N) $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "341--350",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100406X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100406X",
  abstract =     "In [1], the authors prove a conjecture of Calegari and
                 Stein regarding $ \bmod p $ congruences between cusp
                 forms of weight four for \Gamma$_0$ (p) and the
                 derivatives of cusp forms of weight two for the same
                 congruence subgroup. In this paper, we investigate
                 whether or not the result remains valid for cusp forms
                 of level N$_p$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Muic:2011:NVC,
  author =       "Goran Mui{\'c}",
  title =        "On the Non-Vanishing of Certain Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "351--370",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004083",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004083",
  abstract =     "Let \Gamma \subset SL$_2$ ({\mathbb{R}}) be a Fuchsian
                 group of the first kind. In this paper, we study the
                 non-vanishing of the spanning set for the space of
                 cuspidal modular forms of weight m \geq 3 constructed
                 in [5, Corollary 2.6.11]. Our approach is based on the
                 generalization of the non-vanishing criterion for L$^1$
                 Poincar{\'e} series defined for locally compact groups
                 and proved in [6, Theorem 4.1]. We obtain very sharp
                 bounds for the non-vanishing of the spaces of cusp
                 forms for general \Gamma having at least one cusp. We
                 obtain explicit results for congruence subgroups \Gamma
                 (N), \Gamma$_0$ (N), and \Gamma$_1$ (N) (N \geq 1).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bui:2011:CVD,
  author =       "H. M. Bui and Micah B. Milinovich",
  title =        "Central Values of Derivatives of {Dirichlet}
                 {$L$}-Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "371--388",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004125",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004125",
  abstract =     "Let be the set of even, primitive Dirichlet characters
                 (mod q). Using the mollifier method, we show that
                 L$^{(k)}$ (\frac{1}{2}, \chi) \neq 0 for almost all the
                 characters when k and q are large. Here L(s, \chi) is
                 the Dirichlet {$L$}-function associated to the
                 character \chi.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Martin:2011:RTF,
  author =       "Kimball Martin and Mark McKee and Eric Wambach",
  title =        "A Relative Trace Formula for a Compact {Riemann}
                 Surface",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "389--429",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004101",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004101",
  abstract =     "We study a relative trace formula for a compact
                 Riemann surface with respect to a closed geodesic C.
                 This can be expressed as a relation between the period
                 spectrum and the ortholength spectrum of C. This
                 provides a new proof of asymptotic results for both the
                 periods of Laplacian eigenforms along C as well
                 estimates on the lengths of geodesic segments which
                 start and end orthogonally on C. Variant trace formulas
                 also lead to several simultaneous nonvanishing results
                 for different periods.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bundschuh:2011:AND,
  author =       "Peter Bundschuh and Keijo V{\"a}{\"a}n{\"a}nen",
  title =        "An application of {Nesterenko}'s dimension estimate to
                 $p$-adic $q$-series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "431--447",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004071",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004071",
  abstract =     "Very recently, Nesterenko proved a $p$-adic analogue
                 of his famous dimension estimate from 1985. The main
                 aim of our present paper is to use this criterion to
                 obtain lower bounds for the dimension of {$ \mathbb
                 {Q}$}-vector spaces spanned by the values at certain
                 rational points of $p$-adic solutions of a class of
                 linear q-difference equations. For the application of
                 Nesterenko's new estimate, we first need a $p$-adic
                 analogue of T{\"o}pfer's results on entire solutions of
                 such functional equations, and secondly, very precise
                 evaluations of certain $p$-adic Schnirelman
                 integrals.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zorn:2011:EDI,
  author =       "Christian Zorn",
  title =        "Explicit doubling integrals for {$ \mathrm {Sp}_2 (F)
                 $} and {$ \widetilde {\mathrm {Sp}_2}(F) $} using
                 ``good test vectors''",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "449--527",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004046",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004046",
  abstract =     "In this paper, we offer some explicit computations of
                 a formulation of the doubling method of
                 Piatetski-Shapiro and Rallis for the groups Sp$_2$ (F)
                 (the rank 2 symplectic group) and its metaplectic cover
                 for F a finite extension of {$ \mathbb {Q}$}$_p$ with p
                 \neq 2. We determine a set of ``good test vectors'' for
                 the irreducible constituents of unramified principal
                 series representations for these groups as well as a
                 set of ``good theta test sections'' in a family of
                 degenerate principal series representations of Sp$_4$
                 (F) and . Determining ``good test data'' that produces
                 a non-vanishing doubling integral should indicate the
                 existence of a non-vanishing theta lifts for dual pairs
                 of the type (Sp$_2$ (F), O(V)) (respectively) where V
                 is a quadratic space of an even (respectively odd)
                 dimension.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mori:2011:PSE,
  author =       "Andrea Mori",
  title =        "Power Series Expansions of Modular Forms and Their
                 Interpolation Properties",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "2",
  pages =        "529--577",
  month =        mar,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004095",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004095",
  abstract =     "We define a power series expansion of an holomorphic
                 modular form $f$ in the $p$-adic neighborhood of a CM
                 point $x$ of type $K$ for a split good prime $p$. The
                 modularity group can be either a classical conguence
                 group or a group of norm $1$ elements in an order of an
                 indefinite quaternion algebra. The expansion
                 coefficients are shown to be closely related to the
                 classical Maass operators and give $p$-adic information
                 on the ring of definition of $f$. By letting the CM
                 point $x$ vary in its Galois orbit, the $r$-th
                 coefficients define a $p$-adic $ K^\times $-modular
                 form in the sense of Hida. By coupling this form with
                 the $p$-adic avatars of algebraic Hecke characters
                 belonging to a suitable family and using a
                 Rankin--Selberg type formula due to Harris and Kudla
                 along with some explicit computations of Watson and of
                 Prasanna, we obtain in the even weight case a $p$-adic
                 measure whose moments are essentially the square roots
                 of a family of twisted special values of the
                 automorphic $L$-function associated with the base
                 change of $f$ to $K$.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pollack:2011:ESP,
  author =       "Paul Pollack",
  title =        "The Exceptional Set in the Polynomial {Goldbach}
                 Problem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "579--591",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111004423",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004423",
  abstract =     "For each natural number N, let R(N) denote the number
                 of representations of N as a sum of two primes. Hardy
                 and Littlewood proposed a plausible asymptotic formula
                 for R(2N) and showed, under the assumption of the
                 Riemann Hypothesis for Dirichlet {$L$}-functions, that
                 the formula holds ``on average'' in a certain sense.
                 From this they deduced (under ERH) that all but
                 O$_{\epsilon }$ (x$^{1 / 2 + \epsilon }$) of the even
                 natural numbers in [1, x] can be written as a sum of
                 two primes. We generalize their results to the setting
                 of polynomials over a finite field. Owing to Weil's
                 Riemann Hypothesis, our results are unconditional.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bugeaud:2011:MCC,
  author =       "Yann Bugeaud and Alan Haynes and Sanju Velani",
  title =        "Metric Considerations Concerning the Mixed
                 {Littlewood} Conjecture",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "593--609",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004289",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004289",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Draziotis:2011:NIP,
  author =       "Konstantinos A. Draziotis",
  title =        "On the number of integer points on the elliptic curve
                 {$ y^2 = x^3 + A x $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "611--621",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004149",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004149",
  abstract =     "It is given an upper bound for the number of the
                 integer points of the elliptic curve y$^2$ = x$^3$ + Ax
                 (A \in {\mathbb{Z}}) and a conjecture of Schmidt is
                 proven for this family of elliptic curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Medina:2011:IPL,
  author =       "Luis A. Medina and Victor H. Moll and Eric S.
                 Rowland",
  title =        "Iterated Primitives of Logarithmic Powers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "623--634",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100423X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100423X",
  abstract =     "The evaluation of iterated primitives of powers of
                 logarithms is expressed in closed form. The expressions
                 contain polynomials with coefficients given in terms of
                 the harmonic numbers and their generalizations. The
                 logconcavity of these polynomials is established.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ziegler:2011:AUS,
  author =       "Volker Ziegler",
  title =        "The Additive {$S$}-Unit Structure of Quadratic
                 Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "635--644",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004216",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004216",
  abstract =     "We consider a variation of the unit sum number problem
                 for quadratic fields and prove various results.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sun:2011:SNC,
  author =       "Zhi-Wei Sun and Roberto Tauraso",
  title =        "On Some New Congruences for Binomial Coefficients",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "645--662",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004393",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004393",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Astaneh-Asl:2011:IHP,
  author =       "Ali Astaneh-Asl and Hassan Daghigh",
  title =        "Independence of {Heegner} Points for Nonmaximal
                 Orders",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "663--669",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004241",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004241",
  abstract =     "The independence of Heegner points associated to
                 distinct imaginary quadratic fields has been shown by
                 Rosen and Silverman. In this paper we show the
                 independence of Heegner points associated to orders
                 with the same conductor in distinct imaginary quadratic
                 fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gekeler:2011:ZDD,
  author =       "Ernst-Ulrich Gekeler",
  title =        "Zero Distribution and Decay at Infinity of {Drinfeld}
                 Modular Coefficient Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "671--693",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004307",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004307",
  abstract =     "Let \Gamma = GL(2, {$ \mathbb {F} $}$_q$ [T]) be the
                 Drinfeld modular group, which acts on the rigid
                 analytic upper half-plane \Omega. We determine the
                 zeroes of the coefficient modular forms$_a$ \ell$_k$ on
                 the standard fundamental domain for \Gamma on \Omega,
                 along with the dependence of |$_a$ \ell$_k$ (z)| on.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Widmer:2011:NFN,
  author =       "Martin Widmer",
  title =        "On Number Fields with Nontrivial Subfields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "695--720",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004204",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004204",
  abstract =     "What is the probability for a number field of
                 composite degree d to have a nontrivial subfield? As
                 the reader might expect the answer heavily depends on
                 the interpretation of probability. We show that if the
                 fields are enumerated by the smallest height of their
                 generators the probability is zero, at least if d > 6.
                 This is in contrast to what one expects when the fields
                 are enumerated by the discriminant. The main result of
                 this paper is an estimate for the number of algebraic
                 numbers of degree d = en and bounded height which
                 generate a field that contains an unspecified subfield
                 of degree e. If n > {maxe$^2$ + e, 10}, we get the
                 correct asymptotics as the height tends to infinity.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Maire:2011:PLE,
  author =       "Christian Maire",
  title =        "Plongements locaux et extensions de corps de nombres.
                 ({French}) [{Local} embeddings and number field
                 extensions]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "721--738",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004332",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004332",
  abstract =     "Dans ce travail, nous nous int{\'e}ressons au
                 plongement des T-unit{\'e}s d'un corps de nombres K
                 dans une partie de ses compl{\'e}t{\'e}s $p$-adiques
                 construite sur l'ensemble S. Nous montrons que
                 l'injectivit{\'e} de permet d'obtenir des informations
                 sur la structure du groupe de Galois de certaines
                 extensions de K o{\`u} la ramification est li{\'e}e
                 {\`a} S et la d{\'e}composition {\`a} T. Nous
                 {\'e}tudions {\'e}galement le comportement asymptotique
                 du noyau de le long d'une extension $p$-adique
                 analytique sans $p$-torsion. In this article, we are
                 interested in the embedding of the T-units of a number
                 field K in some part of its $p$-adic completions at S.
                 We show that the injectivity of allows us to obtain
                 some information on the structure of the Galois group
                 of some extensions of K where the ramification is
                 attached at S and the decomposition at T. Moreover, we
                 study the asymptotic behavior of the kernel along a
                 $p$-adic analytic extension.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Zywina:2011:RKC,
  author =       "David Zywina",
  title =        "A Refinement of {Koblitz}'s Conjecture",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "739--769",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004411",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004411",
  abstract =     "Let E be an elliptic curve over the rationals. In
                 1988, Koblitz conjectured an asymptotic for the number
                 of primes $p$ for which the cardinality of the group of
                 {$ \mathbb {F} $}$_p$-points of $E$ is prime. However,
                 the constant occurring in his asymptotic does not take
                 into account that the distributions of the $ |E(\mathbb
                 {F}_p)|$ need not be independent modulo distinct
                 primes. We shall describe a corrected constant. We also
                 take the opportunity to extend the scope of the
                 original conjecture to ask how often $ |E(\mathbb
                 {F}_p)| / t$ is an integer and prime for a fixed
                 positive integer $t$, and to consider elliptic curves
                 over arbitrary number fields. Several worked out
                 examples are provided to supply numerical evidence for
                 the new conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Odzak:2011:IFG,
  author =       "Almasa Od{\v{z}}ak and Lejla Smajlovi{\'c}",
  title =        "On interpolation functions for generalized {Li}
                 coefficients in the {Selberg} class",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "771--792",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004356",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004356",
  abstract =     "We prove that there exists an entire complex function
                 of order one and finite exponential type that
                 interpolates the Li coefficients \lambda$_F$ (n)
                 attached to a function F in the class that contains
                 both the Selberg class of functions and
                 (unconditionally) the class of all automorphic
                 {$L$}-functions attached to irreducible, cuspidal,
                 unitary representations of GL$_n$ ({$ \mathbb {Q}$}).
                 We also prove that the interpolation function is
                 (essentially) unique, under generalized Riemann
                 hypothesis. Furthermore, we obtain entire functions of
                 order one and finite exponential type that interpolate
                 both archimedean and non-archimedean contribution to
                 \lambda$_F$ (n) and show that those functions can be
                 interpreted as zeta functions built, respectively, over
                 trivial zeros and all zeros of a function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kaavya:2011:CPP,
  author =       "S. J. Kaavya",
  title =        "Crank $0$ Partitions and the Parity of the Partition
                 Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "793--801",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004381",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004381",
  abstract =     "A well-known problem regarding the integer partition
                 function p(n) is the {\em parity problem\/}, how often
                 is p(n) even or odd? Motivated by this problem, we
                 obtain the following results: (1) A generating function
                 for the number of crank 0 partitions of n. (2) An
                 involution on the crank 0 partitions whose fixed points
                 are called {\em invariant\/} partitions. We then derive
                 a generating function for the number of invariant
                 partitions. (3) A generating function for the number of
                 self-conjugate rank 0 partitions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gallegos-Ruiz:2011:IPH,
  author =       "Homero R. Gallegos-Ruiz",
  title =        "{$S$}-integral points on hyperelliptic curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "803--824",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004435",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004435",
  abstract =     "Let C : Y$^2$ = a$_n$ X$^n$ + \cdots + a$_0$ be a
                 hyperelliptic curve with the a$_i$ rational integers, n
                 \geq 5, and the polynomial on the right irreducible.
                 Let J be its Jacobian. Let S be a finite set of
                 rational primes. We give a completely explicit upper
                 bound for the size of the S-integral points on the
                 model C, provided we know at least one rational point
                 on C and a Mordell--Weil basis for J({$ \mathbb {Q}$}).
                 We use a refinement of the Mordell--Weil sieve which,
                 combined with the upper bound, is capable of
                 determining all the S-integral points. The method is
                 illustrated by determining the S-integral points on the
                 genus 2 hyperelliptic model Y$^2$- Y = X$^5$ X for the
                 set S of the first 22 primes.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bringmann:2011:EFC,
  author =       "Kathrin Bringmann and Olav K. Richter",
  title =        "Exact Formulas for Coefficients of {Jacobi} Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "825--833",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004617",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004617",
  abstract =     "In previous work, we introduced harmonic Maass--Jacobi
                 forms. The space of such forms includes the classical
                 Jacobi forms and certain Maass--Jacobi--Poincar{\'e}
                 series, as well as Zwegers' real-analytic Jacobi forms,
                 which play an important role in the study of mock theta
                 functions and related objects. Harmonic Maass--Jacobi
                 forms decompose naturally into holomorphic and
                 non-holomorphic parts. In this paper, we give exact
                 formulas for the Fourier coefficients of the
                 holomorphic parts of harmonic Maass--Jacobi forms and,
                 in particular, we obtain explicit formulas for the
                 Fourier coefficients of weak Jacobi forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Meemark:2011:DSM,
  author =       "Yotsanan Meemark and Nawaphon Maingam",
  title =        "The Digraph of the Square Mapping on Quotient Rings
                 Over the {Gaussian} Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "835--852",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004459",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004459",
  abstract =     "In this work, we investigate the structure of the
                 digraph associated with the square mapping on the ring
                 of Gaussian integers by using the exponent of the unit
                 group modulo \gamma. The formula for the fixed points
                 of is established. Some connections of the lengths of
                 cycles with the exponent of the unit group modulo
                 \gamma are presented. Furthermore, we study the maximum
                 distance from the cycle on each component.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Han:2011:APF,
  author =       "Jeong Soon Han and Hee Sik Kim and J. Neggers",
  title =        "Acknowledgment of priority: {``The Fibonacci-norm of a
                 positive integer: Observations and conjectures''}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "3",
  pages =        "853--854",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004927",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See \cite{Han:2010:FNP}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004927",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Flicker:2011:CFP,
  author =       "Yuval Z. Flicker",
  title =        "Cusp forms on {$ \mathrm {GSp}(4) $} with {$ \mathrm
                 {SO}(4) $}-periods",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "855--919",
  month =        jun,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111004186",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004186",
  abstract =     "The Saito--Kurokawa lifting of automorphic
                 representations from PGL(2) to the projective
                 symplectic group of similitudes PGSp(4) of genus 2 is
                 studied using the Fourier summation formula (an
                 instance of the ``relative trace formula''), thus
                 characterizing the image as the representations with a
                 nonzero period for the special orthogonal group SO(4,
                 E/F) associated to a quadratic extension E of the
                 global base field F, and a nonzero Fourier coefficient
                 for a generic character of the unipotent radical of the
                 Siegel parabolic subgroup. The image is nongeneric and
                 almost everywhere nontempered, violating a naive
                 generalization of the Ramanujan conjecture. Technical
                 advances here concern the development of the summation
                 formula and matching of relative orbital integrals.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Schwartz:2011:SAP,
  author =       "Ryan Schwartz and J{\'o}zsef Solymosi and Frank {De
                 Zeeuw}",
  title =        "Simultaneous Arithmetic Progressions on Algebraic
                 Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "921--931",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004198",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004198",
  abstract =     "A {\em simultaneous arithmetic progression\/} (s.a.p.)
                 of length k consists of k points (x$_i$, y$_{\sigma
                 (i)}$), where and are arithmetic progressions and
                 \sigma is a permutation. Garcia-Selfa and Tornero asked
                 whether there is a bound on the length of an s.a.p. on
                 an elliptic curve in Weierstrass form over {$ \mathbb
                 {Q}$}. We show that 4319 is such a bound for curves
                 over {\mathbb{R}}. This is done by considering
                 translates of the curve in a grid as a graph. A simple
                 upper bound is found for the number of crossings and
                 the ``crossing inequality'' gives a lower bound.
                 Together these bound the length of an s.a.p. on the
                 curve. We also extend this method to bound the k for
                 which a real algebraic curve can contain k points from
                 a k $ \times $ k grid. Lastly, these results are
                 extended to complex algebraic curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Griffin:2011:DPC,
  author =       "Michael Griffin",
  title =        "Divisibility Properties of Coefficients of Weight $0$
                 Weakly Holomorphic Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "933--941",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004599",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004599",
  abstract =     "In 1949, Lehner showed that certain coefficients of
                 the modular invariant j(\tau) are divisible by high
                 powers of small primes. Kolberg refined Lehner's
                 results and proved congruences for these coefficients
                 modulo high powers of these primes. We extend Lehner's
                 and Kolberg's work to the elements of a canonical basis
                 for the space of weight 0 weakly holomorphic modular
                 forms.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hohn:2011:TGR,
  author =       "Gerald H{\"o}hn",
  title =        "On a Theorem of {Garza} Regarding Algebraic Numbers
                 with Real Conjugates",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "943--945",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004320",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004320",
  abstract =     "We give a new proof of a theorem on the height of
                 algebraic numbers with real conjugates.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Elsenhans:2011:CSG,
  author =       "Andreas-Stephan Elsenhans and J{\"o}rg Jahnel",
  title =        "Cubic Surfaces with a {Galois} Invariant Pair of
                 {Steiner} Trihedra",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "947--970",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004253",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004253",
  abstract =     "We present a method to construct non-singular cubic
                 surfaces over {$ \mathbb {Q} $} with a Galois invariant
                 pair of Steiner trihedra. We start with cubic surfaces
                 in a form generalizing that of Cayley and Salmon. For
                 these, we develop an explicit version of Galois
                 descent.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Saha:2011:PDR,
  author =       "Abhishek Saha",
  title =        "Prime Density Results for {Hecke} Eigenvalues of a
                 {Siegel} Cusp Form",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "971--979",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004642",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004642",
  abstract =     "Let F \in S$_k$ (Sp(2g, {\mathbb{Z}})) be a cuspidal
                 Siegel eigenform of genus g with normalized Hecke
                 eigenvalues \mu$_F$ (n). Suppose that the associated
                 automorphic representation \pi$_F$ is locally tempered
                 everywhere. For each c > 0, we consider the set of
                 primes p for which |\mu$_F$ (p)| \geq c and we provide
                 an explicit upper bound on the density of this set. In
                 the case g = 2, we also provide an explicit upper bound
                 on the density of the set of primes p for which \mu$_F$
                 (p) \geq c.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Miyazaki:2011:TCE,
  author =       "Takafumi Miyazaki",
  title =        "{Terai}'s Conjecture on Exponential {Diophantine}
                 Equations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "981--999",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004496",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004496",
  abstract =     "Let a, b, c be relatively prime positive integers such
                 that a$^p$ + b$^q$ = c$^r$ with fixed integers p, q, r
                 \geq 2. Terai conjectured that the equation a$^x$ +
                 b$^y$ = c$^z$ has no positive integral solutions other
                 than (x, y, z) = (p, q, r) except for specific cases.
                 Most known results on this conjecture concern the case
                 where p = q = 2 and either r = 2 or odd r \geq 3. In
                 this paper, we consider the case where p = q = 2 and r
                 > 2 is even, and partially verify Terai's conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Billerey:2011:CIP,
  author =       "Nicolas Billerey",
  title =        "Crit{\`e}res d'irr{\'e}ductibilit{\'e} pour les
                 repr{\'e}sentations des courbes elliptiques. ({French})
                 [{Irreducibility} criteria for the representations of
                 elliptic curves]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1001--1032",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004538",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004538",
  abstract =     "Soit E une courbe elliptique d{\'e}finie sur un corps
                 de nombres K. On dit qu'un nombre premier p est
                 r{\'e}ductible pour le couple (E, K) si E admet une
                 $p$-isog{\'e}nie d{\'e}finie sur K. L'ensemble de tous
                 ces nombres premiers est fini si et seulement si E n'a
                 pas de multiplication complexe d{\'e}finie sur K. Dans
                 cet article, on montre que l'ensemble des nombres
                 premiers r{\'e}ductibles pour le couple (E, K) est
                 contenu dans l'ensemble des diviseurs premiers d'une
                 liste explicite d'entiers (d{\'e}pendant de E et de K)
                 dont une infinit{\'e} d'entre eux est non nulle. Cela
                 fournit un algorithme efficace de calcul dans le cas
                 fini. D'autres crit{\`e}res moins g{\'e}n{\'e}raux,
                 mais n{\'e}anmoins utiles sont donn{\'e}s ainsi que de
                 nombreux exemples num{\'e}riques. Let E be an elliptic
                 curve defined over a number field K. We say that a
                 prime number p is reducible for (E, K) if E admits a
                 $p$-isogeny defined over K. The so-called reducible set
                 of all such prime numbers is finite if and only if E
                 does not have complex multiplication over K. In this
                 paper, we prove that the reducible set is included in
                 the set of prime divisors of an explicit list of
                 integers (depending on E and K), infinitely many of
                 them being non-zero. It provides an efficient algorithm
                 for computing it in the finite case. Other less general
                 but rather useful criteria are given, as well as many
                 numerical examples.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Hassen:2011:ZFR,
  author =       "Abdul Hassen and Hieu D. Nguyen",
  title =        "A Zero-Free Region for Hypergeometric Zeta Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1033--1043",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004678",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004678",
  abstract =     "This paper investigates the location of ``trivial''
                 zeros of some hypergeometric zeta functions. Analogous
                 to Riemann's zeta function, we demonstrate that they
                 possess a zero-free region on a left-half complex
                 plane, except for infinitely many zeros regularly
                 spaced on the negative real axis.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ghosh:2011:KGT,
  author =       "Anish Ghosh",
  title =        "A {Khintchine--Groshev} theorem for affine
                 hyperplanes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1045--1064",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004228",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004228",
  abstract =     "We prove the divergence case of the
                 Khintchine--Groshev theorem for a large class of affine
                 hyperplanes, completing the convergence case proved in
                 [11] and answering in part a question of Beresnevich
                 {\em et al.\/} ([4]). We use the mechanism of regular
                 systems developed in [4] and estimates from [11].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gun:2011:AIV,
  author =       "Sanoli Gun and M. Ram Murty and Purusottam Rath",
  title =        "Algebraic Independence of Values of Modular Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1065--1074",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004769",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004769",
  abstract =     "We investigate values of modular forms with algebraic
                 Fourier coefficients at algebraic arguments. As a
                 consequence, we conclude about the nature of zeros of
                 such modular forms. In particular, the singular values
                 of modular forms (that is, values at CM points) are
                 related to the recent work of Nesterenko. As an
                 application, we deduce the transcendence of critical
                 values of certain Hecke $L$-series. We also discuss how
                 these investigations generalize to the case of
                 quasi-modular forms with algebraic Fourier
                 coefficients.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Mera:2011:ZFR,
  author =       "Mitsugu Mera",
  title =        "Zero-free regions of a $q$-analogue of the complete
                 {Riemann} zeta function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1075--1092",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004344",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004344",
  abstract =     "A q-analogue of the complete Riemann zeta function
                 presented in this paper is defined by the q-Mellin
                 transform of the Jacobi theta function. We study
                 zero-free regions of the q-zeta function. As a
                 by-product, we show that the Riemann zeta function does
                 not vanish in a sub-region of the critical strip.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cao:2011:SDR,
  author =       "Wei Cao",
  title =        "A Special Degree Reduction of Polynomials Over Finite
                 Fields with Applications",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1093--1102",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004277",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004277",
  abstract =     "Let f be a polynomial in n variables over the finite
                 field {$ \mathbb {F} $}$_q$ and N$_q$ (f) denote the
                 number of {$ \mathbb {F} $}$_q$-rational points on the
                 affine hypersurface f = 0 in {$ \mathbb {A} $}$^n$ ({$
                 \mathbb {F} $}$_q$). A \phi -reduction of f is defined
                 to be a transformation \sigma : {$ \mathbb {F} $}$_q$
                 [x$_1$, \ldots, x$_n$ ] \rightarrow {$ \mathbb {F}
                 $}$_q$ [x$_1$, \ldots, x$_n$ ] such that N$_q$ (f) =
                 N$_q$ (\sigma(f)) and deg f \geq deg \sigma(f). In this
                 paper, we investigate \phi -reduction by using the
                 degree matrix which is formed by the exponents of the
                 variables of f. With \phi -reduction, we may improve
                 various estimates on N$_q$ (f) and utilize the known
                 results for polynomials with low degree. Furthermore,
                 it can be used to find the explicit formula for N$_q$
                 (f).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Raji:2011:ECT,
  author =       "Wissam Raji",
  title =        "{Eichler} Cohomology Theorem for Generalized Modular
                 Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "4",
  pages =        "1103--1113",
  month =        jun,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004514",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:25 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004514",
  abstract =     "We show starting with relations between Fourier
                 coefficients of weakly parabolic generalized modular
                 forms of negative weight that we can construct
                 automorphic integrals for large integer weights. We
                 finally prove an Eichler isomorphism theorem for weakly
                 parabolic generalized modular forms using the classical
                 approach as in [3].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Freiman:2011:SSC,
  author =       "Gregory A. Freiman and Yonutz V. Stanchescu",
  title =        "Sets with Several Centers of Symmetry",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1115--1135",
  month =        aug,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111004174",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004174",
  abstract =     "Let A be a finite subset of the group
                 {\mathbb{Z}}$^2$. Let C = {c$_0$, c$_1$, \ldots, c$_{s
                 - 1}$ } be a finite set of s distinct points in the
                 plane. For every 0 \leq i \leq s -1, we define D$_i$ =
                 {a - a\prime : a \in A, a\prime \in A, a + a\prime =
                 2c$_i$ } and R$_s$ (A) = |D$_0$ \cup D$_1$ \cup \ldots
                 \cup D$_{s - 1}$ |. In [1, 2], we found the maximal
                 value of R$_s$ (A) in cases s = 1, s = 2 and s = 3 and
                 studied the structure of A assuming that R$_3$ (A) is
                 equal or close to its maximal value. In this paper, we
                 examine the case of s = 4 centers of symmetry and we
                 find the {\em maximal value\/} of R$_4$ (A). Moreover,
                 in cases when the maximal value is attained, we will
                 describe the {\em structure of extremal sets}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Tu:2011:ONA,
  author =       "Fang-Ting Tu",
  title =        "On Orders of {$ M(2, K) $} Over a Non--{Archimedean}
                 Local Field",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1137--1149",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004654",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004654",
  abstract =     "Let K be a non-Archimedean local field. In this paper,
                 we first show that if an order in M(2, K) is the
                 intersection of (finitely many) maximal orders in M(2,
                 K), then it is the intersection of at most three
                 maximal orders. Using this result, we obtain a complete
                 classification of orders in M(2, K) that are
                 intersections of maximal orders.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dixit:2011:ATF,
  author =       "Atul Dixit",
  title =        "Analogues of a Transformation Formula of {Ramanujan}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1151--1172",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100454X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100454X",
  abstract =     "We derive two new analogues of a transformation
                 formula of Ramanujan involving the Gamma function and
                 Riemann zeta function present in his \booktitle{Lost
                 Notebook}. Both involve infinite series consisting of
                 Hurwitz zeta functions and yield modular-type
                 relations. As a special case of the first formula, we
                 obtain an identity involving polygamma functions given
                 by A. P. Guinand and as a limiting case of the second
                 formula, we derive the transformation formula of
                 Ramanujan.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ayad:2011:CDV,
  author =       "Mohamed Ayad and Omar Kihel",
  title =        "Common Divisors of Values of Polynomials and Common
                 Factors of Indices in a Number Field",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1173--1194",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004526",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004526",
  abstract =     "Let K be a number field of degree n over {$ \mathbb
                 {Q} $}, {\^A} be the set of integers of K that are
                 primitive over {$ \mathbb {Q} $} and let I(K) be its
                 index. The prime factors of I(K) are called common
                 factors of indices or inessential discriminant
                 divisors. We show that these primes divide another
                 index i(K) previously defined by Gunji and McQuillan as
                 i(K) = lcm$_{\theta \in {\^ A}}$ i(\theta), where
                 i(\theta) = gcd$_{x \in {\mathbb {Z}}}$ F$_{\theta }$
                 (x) and F$_{\theta }$ (x) is the characteristic
                 polynomial of \theta over {$ \mathbb {Q}$}. It is shown
                 that there exists \theta \in {\^A} such that i(K) =
                 i(\theta) and an algorithm is given for the computation
                 of such an integer. For any prime p|i(K), an integer
                 \rho$_K$ (p) defined as the number of such that
                 p|i(\theta) is investigated. It is shown that this
                 integer determines in some cases the splitting type of
                 p in K. Some open questions related to I(K), i(K) and
                 \rho$_K$ (p) are stated.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Philippon:2011:AFC,
  author =       "Patrice Philippon",
  title =        "Approximations fonctionnelles des courbes des espaces
                 projectifs. ({French}) [{Functional} approximations of
                 the curves of projective spaces]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1195--1215",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004502",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004502",
  abstract =     "Algebraic approximation to points in projective spaces
                 offers a new and more flexible approach to algebraic
                 independence theory. When working over the field of
                 algebraic numbers, it leads to open conjectures in
                 higher dimension extending known results in Diophantine
                 approximation. We show here that over the algebraic
                 closure of a function field in one variable, the analog
                 of these conjectures is true. We also derive transfer
                 lemmas which have applications in the study of
                 multiplicity estimates, for example.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Dubickas:2011:RPD,
  author =       "Art{\=u}ras Dubickas",
  title =        "Roots of Polynomials with Dominant Term",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1217--1228",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004575",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004575",
  abstract =     "We characterize all algebraic numbers which are roots
                 of integer polynomials with a coefficient whose modulus
                 is greater than or equal to the sum of moduli of all
                 the remaining coefficients. It turns out that these
                 numbers are zero, roots of unity and those algebraic
                 numbers \beta whose conjugates over {$ \mathbb {Q} $}
                 (including \beta itself) do not lie on the circle |z| =
                 1. We also describe all algebraic integers with norm B
                 which are roots of an integer polynomial with constant
                 coefficient B and the sum of moduli of all other
                 coefficients at most |B|. In contrast to the above, the
                 set of such algebraic integers is ``quite small''.
                 These results are motivated by a recent paper of
                 Frougny and Steiner on the so-called minimal weight
                 \beta -expansions and are also related to some work on
                 canonical number systems and tilings.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Boylan:2011:VFC,
  author =       "Matthew Boylan and Sharon Anne Garthwaite and John
                 Webb",
  title =        "On the Vanishing of {Fourier} Coefficients of Certain
                 Genus Zero Newforms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1229--1245",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004290",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004290",
  abstract =     "Given a classical modular form f(z), a basic question
                 is whether any of its Fourier coefficients vanish. This
                 question remains open for certain modular forms. For
                 example, let \Delta (z) = \Sigma \Gamma (n)q$^n$ \in
                 S$_{12}$ (\Gamma$_0$ (1)). A well-known conjecture of
                 Lehmer asserts that \tau (n) \neq 0 for all n. In
                 recent work, Ono constructed a family of polynomials
                 A$_n$ (x) \in {$ \mathbb {Q}$}[x] with the property
                 that \tau (n) vanishes if and only if A$_n$ (0) and
                 A$_n$ (1728) do. In this paper, we establish a similar
                 criterion for the vanishing of coefficients of certain
                 newforms on genus zero groups of prime level.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ghitza:2011:DHE,
  author =       "Alexandru Ghitza",
  title =        "Distinguishing {Hecke} Eigenforms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1247--1253",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004708",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004708",
  abstract =     "We revisit a theorem of Ram Murty about the number of
                 initial Fourier coefficients that two cuspidal
                 eigenforms of different weights can have in common. We
                 prove an explicit upper bound on this number, and give
                 better conditional and unconditional asymptotic upper
                 bounds. Finally, we describe a numerical experiment
                 testing the sharpness of the upper bound in the case of
                 forms of level one.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Williams:2011:SFO,
  author =       "H. C. Williams and R. K. Guy",
  title =        "Some Fourth-Order Linear Divisibility Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1255--1277",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004587",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004587",
  abstract =     "We extend the Lucas--Lehmer theory for second-order
                 divisibility sequences to a large class of fourth-order
                 sequences, with appropriate laws of apparition and of
                 repetition. Examples are provided by the numbers of
                 perfect matchings, or of spanning trees, in families of
                 graphs, and by the numbers of points on elliptic curves
                 over finite fields. Whether there are fourth-order
                 divisibility sequences not covered by our theory is an
                 open question.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Liu:2011:GUN,
  author =       "Huaning Liu",
  title =        "{Gowers} Uniformity Norm and Pseudorandom Measures of
                 the Pseudorandom Binary Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1279--1302",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004137",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004137",
  abstract =     "Recently there has been much progress in the study of
                 arithmetic progressions. An important tool in these
                 developments is the Gowers uniformity norm. In this
                 paper we study the Gowers norm for pseudorandom binary
                 sequences, and establish some connections between these
                 two subjects. Some examples are given to show that the
                 ``good'' pseudorandom sequences have small Gowers norm.
                 Furthermore, we introduce two large families of
                 pseudorandom binary sequences constructed by the
                 multiplicative inverse and additive character, and
                 study the pseudorandom measures and the Gowers norm of
                 these sequences by using the estimates of exponential
                 sums and properties of the Vandermonde determinant. Our
                 constructions are superior to the previous ones from
                 some points of view.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Dahmen:2011:RMA,
  author =       "Sander R. Dahmen",
  title =        "A refined modular approach to the {Diophantine}
                 equation $ x^2 + y^{2 n} = z^3 $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1303--1316",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004472",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004472",
  abstract =     "Let n be a positive integer and consider the
                 Diophantine equation of generalized Fermat type x$^2$ +
                 y$^{2n}$ = z$^3$ in nonzero coprime integer unknowns
                 x,y,z. Using methods of modular forms and Galois
                 representations for approaching Diophantine equations,
                 we show that for n \in {5,31} there are no solutions to
                 this equation. Combining this with previously known
                 results, this allows a complete description of all
                 solutions to the Diophantine equation above for n \leq
                 10$^7$. Finally, we show that there are also no
                 solutions for n \equiv -1 (mod 6).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Liu:2011:DTS,
  author =       "Zhixin Liu and Guangshi L{\"u}",
  title =        "Density of Two Squares of Primes and Powers of $2$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1317--1329",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004605",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004605",
  abstract =     "As the generalization of the problem of Romanoff, we
                 establish that a positive proportion of integers can be
                 written as the sum of two squares of primes and two
                 powers of 2. We also prove that every large even
                 integer can be written as the sum of two primes and 12
                 powers of 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Baruah:2011:SCD,
  author =       "Nayandeep Deka Baruah and Kanan Kumari Ojah",
  title =        "Some Congruences Deducible from {Ramanujan}'s Cubic
                 Continued Fraction",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1331--1343",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004745",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004745",
  abstract =     "We present some interesting Ramanujan-type congruences
                 for some partition functions arising from Ramanujan's
                 cubic continued fraction. One of our results states
                 that if p$_3$ (n) is defined by, then p$_3$ (9n + 8)
                 \equiv 0 (mod 3$^4$).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Harada:2011:CSU,
  author =       "Masaaki Harada",
  title =        "Construction of Some Unimodular Lattices with Long
                 Shadows",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1345--1358",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004794",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004794",
  abstract =     "In this paper, we construct odd unimodular lattices in
                 dimensions n = 36,37 having minimum norm 3 and 4s = n -
                 16, where s is the minimum norm of the shadow. We also
                 construct odd unimodular lattices in dimensions n =
                 41,43,44 having minimum norm 4 and 4s = n - 24.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Wang:2011:API,
  author =       "Xinna Wang and Yingchun Cai",
  title =        "An Additive Problem Involving {Piatetski--Shapiro}
                 Primes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1359--1378",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004630",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004630",
  abstract =     "Let P$_r$ denote an almost-prime with at most r prime
                 factors, counted according to multiplicity. In this
                 paper it is proved that there exist infinitely many
                 primes of the form p = [n$^c$ ] such that p + 2 =
                 P$_r$, where r is the least positive integer satisfying
                 certain inequalities. In particular for we have r = 5.
                 This result constitutes an improvement upon that of T.
                 P. Peneva.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Park:2011:ALG,
  author =       "Jeehoon Park",
  title =        "Another look at {Gross--Stark} units over the number
                 field {$ \mathbb {Q} $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1379--1393",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004150",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004150",
  abstract =     "We provide another description of the Gross--Stark
                 units over the rational field {$ \mathbb {Q} $}
                 (studied in [B. Gross, $p$-adic $L$-series at s = 0,
                 {\em J. Fac. Sci. Univ. Tokyo\/} 28(3) (1981)
                 979--994]) which is essentially a Gauss sum, using a
                 $p$-adic multiplicative integral of the {\em $p$-adic
                 Kubota--Leopoldt distribution\/}, and give a simplified
                 proof of the Ferrero--Greenberg theorem (see [B.
                 Ferrero and R. Greenberg, On the behavior of $p$-adic
                 {$L$}-functions at s = 0, {\em Invent. Math.\/} 50(1)
                 (1978/79) 91--102]) for $p$-adic Hurwitz zeta
                 functions. This is a precise analog for {$ \mathbb
                 {Q}$} of Darmon--Dasgupta's work on {\em elliptic units
                 for real quadratic fields\/} (see [H. Darmon and S.
                 Dasgupta, Elliptic units for real quadratic fields,
                 {\em Ann. of Math. (2)\/} 163(1) (2006) 301--346]).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ryan:2011:BTC,
  author =       "Nathan C. Ryan and Gonzalo Tornar{\'i}a",
  title =        "A {B{\"o}cherer}-type conjecture for paramodular
                 forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "5",
  pages =        "1395--1411",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004629",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004629",
  abstract =     "In the 1980s B{\"o}cherer formulated a conjecture
                 relating the central value of the quadratic twists of
                 the spinor {$L$}-function attached to a Siegel modular
                 form F to the coefficients of F. He proved the
                 conjecture when F is a Saito--Kurokawa lift. Later
                 Kohnen and Ku{\ss} gave numerical evidence for the
                 conjecture in the case when F is a rational eigenform
                 that is not a Saito--Kurokawa lift. In this paper we
                 develop a conjecture relating the central value of the
                 quadratic twists of the spinor {$L$}-function attached
                 to a paramodular form and the coefficients of the form.
                 We prove the conjecture in the case when the form is a
                 Gritsenko lift and provide numerical evidence when it
                 is not a lift.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Goldston:2011:JCG,
  author =       "D. A. Goldston and A. H. Ledoan",
  title =        "Jumping Champions and Gaps Between Consecutive
                 Primes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1413--1421",
  month =        sep,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S179304211100471X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100471X",
  abstract =     "The most common difference that occurs among the
                 consecutive primes less than or equal to x is called a
                 jumping champion. Occasionally there are ties.
                 Therefore there can be more than one jumping champion
                 for a given x. In 1999 Odlyzko, Rubinstein and Wolf
                 provided heuristic and empirical evidence in support of
                 the conjecture that the numbers greater than 1 that are
                 jumping champions are 4 and the primorials 2, 6, 30,
                 210, 2310,\ldots. As a step toward proving this
                 conjecture they introduced a second weaker conjecture
                 that any fixed prime p divides all sufficiently large
                 jumping champions. In this paper we extend a method of
                 Erd{\H{o}}s and Straus from 1980 to prove that the
                 second conjecture follows directly from the prime pair
                 conjecture of Hardy and Littlewood.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Djankovic:2011:NFA,
  author =       "Goran Djankovi{\'c}",
  title =        "Nonvanishing of the family of {$ \Gamma_1 (q)
                 $}-automorphic {$L$}-functions at the central point",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1423--1439",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004800",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004800",
  abstract =     "We investigate proportion of nonvanishing central
                 values L(f, 1/2) of {$L$}-functions associated to the
                 basis of holomorphic modular forms of fixed weight k
                 with respect to \Gamma$_1$ (q), in the limit when q
                 \rightarrow \infty along the primes. Motivation is a
                 contrast between \Gamma$_0$ (q) and \Gamma$_1$ (q)
                 families in the sense of underlying harmonic
                 analysis.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Komori:2011:FED,
  author =       "Yasushi Komori and Kohji Matsumoto and Hirofumi
                 Tsumura",
  title =        "Functional Equations for Double {$L$}-Functions and
                 Values at Non-Positive Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1441--1461",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004551",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004551",
  abstract =     "We consider double {$L$}-functions with periodic
                 coefficients and complex parameters. We prove
                 functional equations for them, which is of traditional
                 symmetric form on certain hyperplanes. These are
                 character analogs of our previous result on double
                 zeta-functions. We further evaluate double
                 {$L$}-functions at non-positive integers and construct
                 certain $p$-adic double {$L$}-functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Gao:2011:QAN,
  author =       "Weidong Gao and Alfred Geroldinger and Qinghong Wang",
  title =        "A Quantitative Aspect of Non-Unique Factorizations:
                 the {Narkiewicz} Constants",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1463--1502",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004721",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004721",
  abstract =     "Let K be an algebraic number field with non-trivial
                 class group G and let be its ring of integers. For k
                 \in \mathbb{N} and some real x \geq 1, let F$_k$ (x)
                 denote the number of non-zero principal ideals with
                 norm bounded by x such that a has at most k distinct
                 factorizations into irreducible elements. It is well
                 known that F$_k$ (x) behaves, for x \rightarrow \infty,
                 asymptotically like x(log x)$^{-1 + 1 / |G|}$ (log log
                 x)$^{N k (G)}$. We study N$_k$ (G) with new methods
                 from Combinatorial Number Theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pitoun:2011:CCM,
  author =       "Fr{\'e}d{\'e}ric Pitoun",
  title =        "Conoyaux de capitulation et modules d'{Iwasawa}.
                 ({French}) [{Capitulation} co-kernels and {Iwasawa}
                 modules]",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1503--1517",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004861",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004861",
  abstract =     "Soit F un corps de nombres totalement r{\'e}el et p un
                 premier impair, on note $ K_0 $ = F(\zeta$_p$). Pour n
                 \in \mathbb{N}, $ K_n$ d{\'e}signe le n-i{\`e}me
                 {\'e}tage de la {\mathbb{Z}}$_p$ extension cyclotomique
                 $ K_{\infty }$ /K$_0$, A$_n$ est la $p$-partie du
                 groupe des classes de $ K_n$, et N$_{\infty }$ est
                 l'extension de $ K_{\infty }$ obtenue en extrayant des
                 racines $p$-primaires d'unit{\'e}s. Le but de cet
                 article est de montrer que le dual de Pontryagin de la
                 partie plus des conoyaux de capitulation, sur laquelle
                 l'action de \Gamma a {\'e}t{\'e} tordue une fois par le
                 caract{\`e}re cyclotomique et la partie moins de la
                 {\mathbb{Z}}$_p$ torsion du groupe de Galois
                 Gal(N$_{\infty }$ \cap L$_{\infty }$ /K$_{\infty }$)
                 sont isomorphes. Let F be a totally real number field
                 and p an odd prime, we note $ K_0$ = F(\zeta$_p$). For
                 an integer n, $ K_n$ is the nth floor of the
                 {\mathbb{Z}}$_p$-cyclotomic extension $ K_{\infty }$
                 /K$_0$, A$_n$ is the $p$-part of the class group of $
                 K_n$, and N$_{\infty }$ is the extension of $ K_{\infty
                 }$ generated by $p$-primary roots of units. In this
                 article, we prove that the plus part of the
                 capitulation's cokernel, on which \Gamma -action was
                 twisted on time by the cyclotomic character, and the
                 minus part of the {\mathbb{Z}}$_p$-torsion of the
                 Galois group Gal(N$_{\infty }$ \cap L$_{\infty }$
                 /K$_{\infty }$) is isomorphic.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  language =     "French",
}

@Article{Blache:2011:NPC,
  author =       "R{\'e}gis Blache",
  title =        "{Newton} Polygons for Character Sums and
                 {Poincar{\'e}} Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1519--1542",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004368",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004368",
  abstract =     "In this paper, we precise the asymptotic behavior of
                 Newton polygons of {$L$}-functions associated to
                 character sums, coming from certain n variable Laurent
                 polynomials. In order to do this, we use the free sum
                 on convex polytopes. This operation allows the
                 determination of the limit of generic Newton polygons
                 for the sum \Delta = \Delta$_1$ \oplus \Delta$_2$ when
                 we know the limit of generic Newton polygons for each
                 factor. To our knowledge, these are the first results
                 concerning the asymptotic behavior of Newton polygons
                 for multivariable polynomials when the generic Newton
                 polygon differs from the combinatorial (Hodge) polygon
                 associated to the polyhedron.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Girstmair:2011:CFJ,
  author =       "Kurt Girstmair",
  title =        "Continued Fractions and {Jacobi} Symbols",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1543--1555",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004848",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004848",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ostafe:2011:MCS,
  author =       "Alina Ostafe and Igor E. Shparlinski and Arne
                 Winterhof",
  title =        "Multiplicative Character Sums of a Class of Nonlinear
                 Recurrence Vector Sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1557--1571",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004484",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004484",
  abstract =     "We estimate multiplicative character sums along the
                 orbits of a class of nonlinear recurrence vector
                 sequences. In the one-dimensional case, only much
                 weaker estimates are known and our results have no
                 one-dimensional analogs.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Papikian:2011:GAG,
  author =       "Mihran Papikian",
  title =        "On Generators of Arithmetic Groups Over Function
                 Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1573--1587",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004265",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004265",
  abstract =     "Let F = {$ \mathbb {F} $}$_q$ (T) be the field of
                 rational functions with {$ \mathbb {F}
                 $}$_q$-coefficients, and A = {$ \mathbb {F} $}$_q$ [T]
                 be the subring of polynomials. Let D be a division
                 quaternion algebra over F which is split at 1/T. For
                 certain A-orders in D we find explicit finite sets
                 generating their groups of units.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Xia:2011:DRG,
  author =       "Ernest X. W. Xia and X. M. Yao",
  title =        "The $8$-dissection of the
                 {Ramanujan--G{\"o}llnitz--Gordon} continued fraction by
                 an iterative method",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1589--1593",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004824",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004824",
  abstract =     "In this paper, we present an iterative method to
                 derive the 8-dissections of the
                 Ramanujan--G{\"o}llnitz--Gordon continued fraction and
                 its reciprocal which were first discovered by
                 Hirschhorn.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chen:2011:CP,
  author =       "Yong-Gao Chen and Jing-Rui Lou",
  title =        "The congruent properties for $ r_s(n) $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1595--1602",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004885",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  note =         "See erratum \cite{Chen:2013:ECP}.",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004885",
  abstract =     "Let r$_s$ (n) denote the number of ways to write an
                 integer n as the sum of s squares of integers. In this
                 paper, the congruent properties for r$_s$ (n) are
                 studied. We give the elementary combinatorial proofs of
                 all related results due to Wagstaff and Chen, and
                 obtain some new results.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Oh:2011:RAP,
  author =       "Byeong-Kweon Oh",
  title =        "Representations of Arithmetic Progressions by Positive
                 Definite Quadratic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1603--1614",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004915",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004915",
  abstract =     "For a positive integer d and a non-negative integer a,
                 let S$_{d, a}$ be the set of all integers of the form
                 dn + a for any non-negative integer n. A (positive
                 definite integral) quadratic form f is said to be
                 S$_{d, a}$- {\em universal\/} if it represents all
                 integers in the set S$_{d, a}$, and is said to be
                 S$_{d, a}$- {\em regular\/} if it represents all
                 integers in the non-empty set S$_{d, a}$ \cap Q((f)),
                 where Q(gen(f)) is the set of all integers that are
                 represented by the genus of f. In this paper, we prove
                 that there is a polynomial U(x,y) \in {$ \mathbb
                 {Q}$}[x,y] (R(x,y) \in {$ \mathbb {Q}$}[x,y]) such that
                 the discriminant df for any S$_{d, a}$ universal
                 (S$_{d, a}$-regular) ternary quadratic forms is bounded
                 by U(d,a) (respectively, R(d,a)).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Xiong:2011:TII,
  author =       "Xinhua Xiong",
  title =        "Two Identities Involving the Cubic Partition
                 Function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1615--1626",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004757",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004757",
  abstract =     "We give a very elementary proof of an identity
                 involving the cubic partition function and we also give
                 an elementary proof of a new identity for the cubic
                 partition function which is analogs to Zuckerman's
                 identity for the ordinary partition function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Fukuda:2011:WCN,
  author =       "Takashi Fukuda and Keiichi Komatsu",
  title =        "{Weber}'s class number problem in the cyclotomic {$
                 \mathbb {Z}_2 $}-extension of {$ \mathbb {Q} $},
                 {III}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1627--1635",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004782",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004782",
  abstract =     "Let h$_n$ denote the class number of which is a cyclic
                 extension of degree 2$^n$ over the rational number
                 field {$ \mathbb {Q}$}. There are no known examples of
                 h$_n$ > 1. We prove that a prime number \ell does not
                 divide h$_n$ for all n \geq 1 if \ell is less than
                 10$^9$ or \ell satisfies a congruence relation \ell
                 \nequiv \pm 1 (mod 32).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Sakai:2011:AOP,
  author =       "Yuichi Sakai",
  title =        "The {Atkin} Orthogonal Polynomials for the Low-Level
                 {Fricke} Groups and Their Application",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1637--1661",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004460",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004460",
  abstract =     "Kaneko and Zagier proved the relation between the
                 Atkin orthogonal polynomials and supersingular
                 j-polynomials for PSL$_2$ ({\mathbb{Z}}). Tsutsumi also
                 proved its relation for the Hecke subgroups of level
                 less than or equal to 4. In this paper, we define the
                 Atkin inner product for the Fricke groups of level less
                 than or equal to 3 and construct the Atkin orthogonal
                 polynomials. Then, we give the relation between
                 supersingular -polynomials defined by Koike and its
                 polynomials. We also give extremal quasimodular forms
                 of depth 1 by using its orthogonal polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Turkelli:2011:CMC,
  author =       "Seyfi T{\"u}rkelli",
  title =        "Counting multisections in conic bundles over a curve
                 defined over {$ \mathbb {F}_q $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1663--1680",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100485X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100485X",
  abstract =     "For a given conic bundle X over a curve C defined over
                 {$ \mathbb {F} $}$_q$, we count irreducible branch
                 covers of C in X of degree d and height e \gg 1. As a
                 special case, we get the number of algebraic numbers of
                 degree d and height e over the function field {$
                 \mathbb {F} $}$_q$ (C).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hong:2011:ABS,
  author =       "Shaofang Hong and Raphael Loewy",
  title =        "Asymptotic behavior of the smallest eigenvalue of
                 matrices associated with completely even functions $
                 (\bmod r) $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "6",
  pages =        "1681--1704",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100437X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100437X",
  abstract =     "In this paper, we present systematically analysis on
                 the smallest eigenvalue of matrices associated with
                 completely even functions (mod r). We obtain several
                 theorems on the asymptotic behavior of the smallest
                 eigenvalue of matrices associated with completely even
                 functions (mod r). In particular, we get information on
                 the asymptotic behavior of the smallest eigenvalue of
                 the famous Smith matrices. Finally some examples are
                 given to demonstrate the main results.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Knopfmacher:2011:PPN,
  author =       "Arnold Knopfmacher and Florian Luca",
  title =        "On Prime-Perfect Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1705--1716",
  month =        nov,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111004447",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004447",
  abstract =     "We prove that the Diophantine equation has only
                 finitely many positive integer solutions k, p$_1$,
                 \ldots, p$_k$, r$_1$, \ldots, r$_k$, where p$_1$,
                 \ldots, p$_k$ are distinct primes. If a positive
                 integer n has prime factorization, then represents the
                 number of ordered factorizations of n into prime parts.
                 Hence, solutions to the above Diophantine equation are
                 designated as prime-perfect numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ballot:2011:MD,
  author =       "Christian Ballot and Mireille Car",
  title =        "On {Murata} Densities",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1717--1736",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100440X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100440X",
  abstract =     "In this paper, we set up an abstract theory of Murata
                 densities, well tailored to general arithmetical
                 semigroups. In [On certain densities of sets of primes,
                 {\em Proc. Japan Acad. Ser. A Math. Sci.\/} 56(7)
                 (1980) 351--353; On some fundamental relations among
                 certain asymptotic densities, {\em Math. Rep. Toyama
                 Univ.\/} 4(2) (1981) 47--61], Murata classified certain
                 prime density functions in the case of the arithmetical
                 semigroup of natural numbers. Here, it is shown that
                 the same density functions will obey a very similar
                 classification in any arithmetical semigroup whose
                 sequence of norms satisfies certain general growth
                 conditions. In particular, this classification holds
                 for the set of monic polynomials in one indeterminate
                 over a finite field, or for the set of ideals of the
                 ring of S-integers of a global function field (S
                 finite).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Hare:2011:SD,
  author =       "Kevin G. Hare and Shanta Laishram and Thomas Stoll",
  title =        "The sum of digits of $n$ and $ n^2$",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1737--1752",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004319",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004319",
  abstract =     "Let s$_q$ (n) denote the sum of the digits in the
                 q-ary expansion of an integer n. In 2005, Melfi
                 examined the structure of n such that s$_2$ (n) = s$_2$
                 (n$^2$). We extend this study to the more general case
                 of generic q and polynomials p(n), and obtain, in
                 particular, a refinement of Melfi's result. We also
                 give a more detailed analysis of the special case p(n)
                 = n$^2$, looking at the subsets of n where s$_q$ (n) =
                 s$_q$ (n$^2$) = k for fixed k.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bazzanella:2011:TCR,
  author =       "Danilo Bazzanella",
  title =        "Two Conditional Results About Primes in Short
                 Intervals",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1753--1759",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004563",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004563",
  abstract =     "In 1937, Ingham proved that \psi (x + x$^{\theta }$) -
                 \psi (x) \sim x$^{\theta }$ for x \rightarrow \infty,
                 under the assumption of the Lindel{\"o}f hypothesis for
                 \theta > 1/2. In this paper we examine how the above
                 asymptotic formula holds by assuming in turn two
                 different heuristic hypotheses. It must be stressed
                 that both the hypotheses are implied by the
                 Lindel{\"o}f hypothesis.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Ribenboim:2011:MPT,
  author =       "Paulo Ribenboim",
  title =        "Multiple patterns of $k$-tuples of integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1761--1779",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004733",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004733",
  abstract =     "The first proposition and its corollary are a
                 transfiguration of Dirichlet's pigeon-hole principle.
                 They are applied to show that a wide variety of
                 sequences display arbitrarily large patterns of sums,
                 differences, higher differences, etc. Among these, we
                 include sequences of primes in arithmetic progressions,
                 of powerful integers, sequences of integers with
                 radical index having a prescribed lower bound, and many
                 others. We also deal with patterns in iterated
                 sequences of primes, patterns of gaps between primes,
                 patterns of values of Euler's \phi -function, or their
                 gaps, as well as patterns related to the sequence of
                 Carmichael numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Faber:2011:NRI,
  author =       "Xander Faber and Benjamin Hutz and Michael Stoll",
  title =        "On the Number of Rational Iterated Preimages of the
                 Origin Under Quadratic Dynamical Systems",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1781--1806",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004162",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004162",
  abstract =     "For a quadratic endomorphism of the affine line
                 defined over the rationals, we consider the problem of
                 bounding the number of rational points that eventually
                 land at the origin after iteration. In the article
                 ``Uniform bounds on pre-images under quadratic
                 dynamical systems,'' by two of the present authors and
                 five others, it was shown that the number of rational
                 iterated preimages of the origin is bounded as one
                 varies the morphism in a certain one-dimensional
                 family. Subject to the validity of the Birch and
                 Swinnerton-Dyer conjecture and some other related
                 conjectures for the $L$-series of a specific abelian
                 variety and using a number of modern tools for locating
                 rational points on high genus curves, we show that the
                 maximum number of rational iterated preimages is six.
                 We also provide further insight into the geometry of
                 the ``preimage curves.''",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chambert-Loir:2011:TJS,
  author =       "Antoine Chambert-Loir",
  title =        "The Theorem of {Jentzsch--Szeg{\H{o}}} on an Analytic
                 Curve: Application to the Irreducibility of Truncations
                 of Power Series",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1807--1823",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004691",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004691",
  abstract =     "A theorem of Jentzsch--Szeg{\H{o}} describes the limit
                 measure of a sequence of discrete measures associated
                 to zeroes of a sequence of polynomials in one variable.
                 Following the presentation by Andrievskii and Blatt in
                 [ {\em Discrepancy of Signed Measures and Polynomial
                 Approximation\/}, Springer Monographs in Mathematics
                 (Springer-Verlag, New York, 2002)] we extend this
                 theorem to compact Riemann surfaces and to analytic
                 curves in the sense of Berkovich over ultrametric
                 fields, using classical potential theory in the former
                 case, and Baker/Rumely, Thuillier's potential theory on
                 analytic curves in the latter case. We then apply this
                 equidistribution theorem to the question of
                 irreducibility of truncations of power series with
                 coefficients in ultrametric fields. {\em R{\'e}sum{\'e}
                 fran{\c{c}}ais\/}: Le th{\'e}or{\`e}me de
                 Jentzsch--Szeg{\H{o}} d{\'e}crit la mesure limite d'une
                 suite de mesures discr{\`e}tes associ{\'e}e aux
                 z{\'e}ros d'une suite convenable de polyn{\^o}mes en
                 une variable. Suivant la pr{\'e}sentation que font
                 Andrievskii et Blatt dans [ {\em Discrepancy of Signed
                 Measures and Polynomial Approximation\/}, Springer
                 Monographs in Mathematics (Springer-Verlag, New York,
                 2002)] on {\'e}tend ici ce r{\'e}sultat aux surfaces de
                 Riemann compactes, puis aux courbes analytiques sur un
                 corps ultram{\'e}trique. On donne pour finir quelques
                 corollaires du cas particulier de la droite projective
                 sur un corps ultram{\'e}trique {\`a}
                 l'irr{\'e}ductibilit{\'e} des polyn{\^o}mes-sections
                 d'une s{\'e}rie enti{\`e}re en une variable.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Berger:2011:AFD,
  author =       "Laurent Berger",
  title =        "A $p$-adic family of dihedral {$ (\phi,
                 \Gamma)$}-modules",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1825--1834",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004770",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004770",
  abstract =     "The goal of this paper is to construct explicitly a
                 $p$-adic family of representations (which are dihedral
                 representations), to construct their attached (\phi,
                 \Gamma)-modules by writing down explicit matrices for
                 \phi and for the action of \Gamma, and finally to
                 determine which of these are trianguline.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Zumalacarregui:2011:CPM,
  author =       "Ana Zumalac{\'a}rregui",
  title =        "Concentration of Points on Modular Quadratic Forms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1835--1839",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004897",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004897",
  abstract =     "Let Q(x, y) be a quadratic form with discriminant D
                 \neq 0. We obtain non-trivial upper bound estimates for
                 the number of solutions of the congruence Q(x, y)
                 \equiv \lambda (mod p), where p is a prime and x, y lie
                 in certain intervals of length M, under the assumption
                 that Q(x, y) - \lambda is an absolutely irreducible
                 polynomial modulo p. In particular, we prove that the
                 number of solutions to this congruence is M$^{o(1)}$
                 when M \ll p$^{1 / 4}$. These estimates generalize a
                 previous result by Cilleruelo and Garaev on the
                 particular congruence xy \equiv \lambda (mod p).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Petersen:2011:EAN,
  author =       "Kathleen L. Petersen and Christopher D. Sinclair",
  title =        "Equidistribution of Algebraic Numbers of Norm One in
                 Quadratic Number Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1841--1861",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004666",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004666",
  abstract =     "Given a fixed quadratic extension K of {$ \mathbb {Q}
                 $}, we consider the distribution of elements in K of
                 norm one (denoted ). When K is an imaginary quadratic
                 extension, is naturally embedded in the unit circle in
                 {\mathbb{C}} and we show that it is equidistributed
                 with respect to inclusion as ordered by the absolute
                 Weil height. By Hilbert's Theorem 90, an element in can
                 be written as for some, which yields another ordering
                 of given by the minimal norm of the associated
                 algebraic integers. When K is imaginary we also show
                 that is equidistributed in the unit circle under this
                 norm ordering. When K is a real quadratic extension, we
                 show that is equidistributed with respect to norm,
                 under the map \beta \mapsto log|\beta |(mod
                 log|\epsilon$^2$ |) where \epsilon is a fundamental
                 unit of.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Reznick:2011:STC,
  author =       "Bruce Reznick and Jeremy Rouse",
  title =        "On the Sums of Two Cubes",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1863--1882",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004903",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004903",
  abstract =     "We solve the equation f(x, y)$^3$ + g(x, y)$^3$ =
                 x$^3$ + y$^3$ for homogeneous f, g \in {\mathbb{C}}(x,
                 y), completing an investigation begun by Vi{\`e}te in
                 1591. The usual addition law for elliptic curves and
                 composition give rise to two binary operations on the
                 set of solutions. We show that a particular subset of
                 the set of solutions is ring isomorphic to
                 {\mathbb{Z}}[e$^{2 \pi i / 3}$ ].",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bouganis:2011:NAC,
  author =       "Thanasis Bouganis",
  title =        "Non--{Abelian} Congruences Between Special Values of
                 {$L$}-Functions of Elliptic Curves: the {CM} Case",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1883--1934",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100468X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100468X",
  abstract =     "In this work we prove congruences between special
                 values of {$L$}-functions of elliptic curves with CM
                 that seem to play a central role in the analytic side
                 of the non-commutative Iwasawa theory. These
                 congruences are the analog for elliptic curves with CM
                 of those proved by Kato, Ritter and Weiss for the Tate
                 motive. The proof is based on the fact that the
                 critical values of elliptic curves with CM, or what
                 amounts to the same, the critical values of
                 Gr{\"o}ssencharacters, can be expressed as values of
                 Hilbert--Eisenstein series at CM points. We believe
                 that our strategy can be generalized to provide
                 congruences for a large class of $L$-values.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Li:2011:DCU,
  author =       "Yan Li and Lianrong Ma",
  title =        "Double Coverings and Unit Square Problems for
                 Cyclotomic Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1935--1944",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004836",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004836",
  abstract =     "In this paper, using the theory of double coverings of
                 cyclotomic fields, we give a formula for, where K = {$
                 \mathbb {Q} $}(\zeta$_n$), G = Gal(K/{$ \mathbb {Q}$}),
                 {$ \mathbb {F} $}$_2$ = {\mathbb{Z}}/2{\mathbb{Z}} and
                 U$_K$ is the unit group of K. We explicitly determine
                 all the cyclotomic fields K = {$ \mathbb
                 {Q}$}(\zeta$_n$) such that . Then we apply it to the
                 unit square problem raised in [Y. Li and X. Zhang,
                 Global unit squares and local unit squares, {\em J.
                 Number Theory\/} 128 (2008) 2687--2694]. In particular,
                 we prove that the unit square problem does not hold for
                 {$ \mathbb {Q}$}(\zeta$_n$) if n has more than three
                 distinct prime factors, i.e. for each odd prime p,
                 there exists a unit, which is a square in all local
                 fields {$ \mathbb {Q}$}(\zeta$_n$)$_v$ with v | p but
                 not a square in {$ \mathbb {Q}$}(\zeta$_n$), if n has
                 more than three distinct prime factors.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Huber:2011:DEC,
  author =       "Tim Huber",
  title =        "Differential Equations for Cubic Theta Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1945--1957",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004873",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004873",
  abstract =     "We show that the cubic theta functions satisfy two
                 distinct coupled systems of nonlinear differential
                 equations. The resulting relations are analogous to
                 Ramanujan's differential equations for Eisenstein
                 series on the full modular group. We deduce the cubic
                 analogs presented here from trigonometric series
                 identities arising in Ramanujan's original paper on
                 Eisenstein series. Several consequences of these
                 differential equations are established, including a
                 short proof of a famous cubic theta function identity
                 derived by J. M. Borwein and P. B. Borwein.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Guo:2011:FSA,
  author =       "Victor J. W. Guo and Jiang Zeng",
  title =        "Factors of Sums and Alternating Sums Involving
                 Binomial Coefficients and Powers of Integers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "7",
  pages =        "1959--1976",
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004812",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:26 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004812",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Merila:2011:NLC,
  author =       "Ville Meril{\"a}",
  title =        "A Nonvanishing Lemma for Certain {Pad{\'e}}
                 Approximations of the Second Kind",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "1977--1997",
  month =        dec,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042111004964",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004964",
  abstract =     "We prove the nonvanishing lemma for explicit second
                 kind Pad{\'e} approximations to generalized
                 hypergeometric and q-hypergeometric functions. The
                 proof is based on an evaluation of a generalized
                 Vandermonde determinant. Also, some immediate
                 applications to the Diophantine approximation is given
                 in the form of sharp linear independence measures for
                 hypergeometric E- and G-functions in algebraic number
                 fields with different valuations.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Nathanson:2011:PAN,
  author =       "Melvyn B. Nathanson",
  title =        "Problems in additive number theory, {IV}: Nets in
                 groups and shortest length $g$-adic representations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "1999--2017",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004940",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004940",
  abstract =     "The number theoretic analog of a net in metric
                 geometry suggests new problems and results in
                 combinatorial and additive number theory. For example,
                 for a fixed integer $ g \geq 2 $, the study of $h$-nets
                 in the additive group of integers with respect to the
                 generating set $ A_g = \{ 0 \} \cup \{ \pm g^i \colon i
                 = 0, 1, 2, \ldots \} $ requires a knowledge of the word
                 lengths of integers with respect to $ A_g$. A $g$-adic
                 representation of an integer is described that
                 algorithmically produces a representation of shortest
                 length. Additive complements and additive asymptotic
                 complements are also discussed, together with their
                 associated minimality problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Haessig:2011:FSP,
  author =       "C. Douglas Haessig and Antonio Rojas-Le{\'o}n",
  title =        "{$L$}-Functions of Symmetric Powers of the Generalized
                 {Airy} Family of Exponential Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2019--2064",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005040",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005040",
  abstract =     "This paper looks at the {$L$}-function of the kth
                 symmetric power of the -sheaf Ai$_f$ over the affine
                 line associated to the generalized Airy family of
                 exponential sums. Using \ell -adic techniques, we
                 compute the degree of this rational function as well as
                 the local factors at infinity. Using $p$-adic
                 techniques, we study the $q$-adic Newton polygon of the
                 {$L$}-function.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Pande:2011:DGR,
  author =       "Aftab Pande",
  title =        "Deformations of {Galois} Representations and the
                 Theorems of {Sato--Tate} and {Lang--Trotter}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2065--2079",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004939",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004939",
  abstract =     "We construct infinitely ramified Galois
                 representations \rho such that the a$_l$ (\rho)'s have
                 distributions in contrast to the statements of
                 Sato--Tate, Lang--Trotter and others. Using similar
                 methods we deform a residual Galois representation for
                 number fields and obtain an infinitely ramified
                 representation with very large image, generalizing a
                 result of Ramakrishna.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Bremner:2011:X,
  author =       "Andrew Bremner and Maciej Ulas",
  title =        "On $ x^a \pm y^b \pm z^c \pm w^d = 0 $, $ 1 / a + 1 /
                 b + 1 / c + 1 / d = 1 $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2081--2090",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005076",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005076",
  abstract =     "It is well known that the Diophantine equations x$^4$
                 + y$^4$ = z$^4$ + w$^4$ and x$^4$ + y$^4$ + z$^4$ =
                 w$^4$ each have infinitely many rational solutions. It
                 is also known for the equation x$^6$ + y$^6$- z$^6$ =
                 w$^2$. We extend the investigation to equations x$^a$
                 \pm y$^b$ = \pm z$^c$ \pm w$^d$, a, b, c, d \in Z, with
                 1/a + 1/b + 1/c + 1/d = 1. We show, with one possible
                 exception, that if there is a solution of the equation
                 in the reals, then the equation has infinitely many
                 solutions in the integers. Of particular interest is
                 the equation x$^6$ + y$^6$ + z$^6$ = w$^2$ because of
                 its classical nature; but there seem to be no
                 references in the literature.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Yu:2011:EMO,
  author =       "Chia-Fu Yu",
  title =        "On the Existence of Maximal Orders",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2091--2114",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005003",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005003",
  abstract =     "We generalize the existence of maximal orders in a
                 semi-simple algebra for general ground rings. We also
                 improve several statements in Chaps. 5 and 6 of
                 Reiner's book [ {\em Maximal Orders\/}, London
                 Mathematical Society Monographs, Vol. 5 (Academic
                 Press, London, 1975), 395 pp.] concerning separable
                 algebras by removing the separability condition,
                 provided the ground ring is only assumed to be
                 Japanese, a very mild condition. Finally, we show the
                 existence of maximal orders as endomorphism rings of
                 abelian varieties in each isogeny class.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Qi:2011:MTS,
  author =       "Zhi Qi and Chang Yang",
  title =        "{Morita}'s Theory for the Symplectic Groups",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2115--2137",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004952",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004952",
  abstract =     "We construct and study the holomorphic discrete series
                 representations and the principal series
                 representations of the symplectic group Sp(2n, F) over
                 a $p$-adic field F as well as a duality between some
                 sub-representations of these two representations. The
                 constructions of these two representations generalize
                 those defined in Morita and Murase's works. Moreover,
                 Morita built a duality for SL(2, F) defined by
                 residues. We view the duality we defined as an
                 algebraic interpretation of Morita's duality in some
                 extent and its generalization to the symplectic
                 groups.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Lebacque:2011:LDZ,
  author =       "Philippe Lebacque and Alexey Zykin",
  title =        "On Logarithmic Derivatives of Zeta Functions in
                 Families of Global Fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2139--2156",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005015",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005015",
  abstract =     "We prove a formula for the limit of logarithmic
                 derivatives of zeta functions in families of global
                 fields with an explicit error term. This can be
                 regarded as a rather far reaching generalization of the
                 explicit Brauer--Siegel theorem both for number fields
                 and function fields.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Habsieger:2011:SCP,
  author =       "Laurent Habsieger and Emmanuel Royer",
  title =        "Spiegelungssatz: a Combinatorial Proof for the
                 $4$-Rank",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2157--2170",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005106",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005106",
  abstract =     "The Spiegelungssatz is an inequality between the
                 4-ranks of the narrow ideal class groups of the
                 quadratic fields and . We provide a combinatorial proof
                 of this inequality. Our interpretation gives an affine
                 system of equations that allows to describe precisely
                 some equality cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Vega:2011:HFF,
  author =       "M. Valentina Vega",
  title =        "Hypergeometric Functions Over Finite Fields and Their
                 Relations to Algebraic Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2171--2195",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004976",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004976",
  abstract =     "In this work we present an explicit relation between
                 the number of points on a family of algebraic curves
                 over {$ \mathbb {F} $}$_q$ and sums of values of
                 certain hypergeometric functions over {$ \mathbb {F}
                 $}$_q$. Moreover, we show that these hypergeometric
                 functions can be explicitly related to the roots of the
                 zeta function of the curve over {$ \mathbb {F} $}$_q$
                 in some particular cases. A general conjecture relating
                 these last two is presented and advances toward its
                 proof are shown in the last section.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Jabuka:2011:WTD,
  author =       "Stanislav Jabuka and Sinai Robins and Xinli Wang",
  title =        "When Are Two {Dedekind} Sums Equal?",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2197--2202",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005088",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005088",
  abstract =     "A natural question about Dedekind sums is to find
                 conditions on the integers a$_1$, a$_2$, and b such
                 that s(a$_1$, b) = s(a$_2$, b). We prove that if the
                 former equality holds then b|(a$_1$ a$_2$- 1)(a$_1$-
                 a$_2$). Surprisingly, to the best of our knowledge such
                 statements have not appeared in the literature. A
                 similar theorem is proved for the more general
                 Dedekind--Rademacher sums as well, namely that for any
                 fixed non-negative integer n, a positive integer
                 modulus b, and two integers a$_1$ and a$_2$ that are
                 relatively prime to b, the hypothesis r$_n$ (a$_1$, b)
                 = r$_n$ (a$_2$, b) implies that b|(6n$^2$ + 1 - a$_1$
                 a$_2$)(a$_2$- a$_1$).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Smith:2011:VBD,
  author =       "Ethan Smith",
  title =        "A Variant of the {Barban--Davenport--Halberstam
                 Theorem}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2203--2218",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100499X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100499X",
  abstract =     "Let L/K be a Galois extension of number fields. The
                 problem of counting the number of prime ideals {$
                 \mathfrak {p} $} of K with fixed Frobenius class in
                 Gal(L/K) and norm satisfying a congruence condition is
                 considered. We show that the square of the error term
                 arising from the Chebotar{\"e}v Density Theorem for
                 this problem is small ``on average''. The result may be
                 viewed as a variation on the classical
                 Barban--Davenport--Halberstam Theorem.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Harvey:2011:CDI,
  author =       "M. P. Harvey",
  title =        "Cubic {Diophantine} Inequalities Involving a Norm
                 Form",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2219--2235",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005052",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005052",
  abstract =     "We apply Freeman's variant of the Davenport--Heilbronn
                 method to provide an asymptotic formula for the number
                 of small values taken by a certain family of cubic
                 forms with real coefficients. The cubic forms in
                 question arise as the sum of a diagonal form and a norm
                 form and should have at least seven variables.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Rolen:2011:GCN,
  author =       "Larry Rolen",
  title =        "A Generalization of the Congruent Number Problem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2237--2247",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005039",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005039",
  abstract =     "We study a certain generalization of the classical
                 Congruent Number Problem. Specifically, we study
                 integer areas of rational triangles with an arbitrary
                 fixed angle \theta. These numbers are called \theta
                 -congruent. We give an elliptic curve criterion for
                 determining whether a given integer n is \theta
                 congruent. We then consider the ``density'' of integers
                 n which are \theta -congruent, as well as the related
                 problem giving the ``density'' of angles \theta for
                 which a fixed n is congruent. Assuming the
                 Shafarevich--Tate conjecture, we prove that both
                 proportions are at least 50\% in the limit. To obtain
                 our result we use the recently proven $p$-parity
                 conjecture due to Monsky and the Dokchitsers as well as
                 a theorem of Helfgott on average root numbers in
                 algebraic families.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Radu:2011:CPM,
  author =       "Silviu Radu and James A. Sellers",
  title =        "Congruence properties modulo $5$ and $7$ for the {$
                 \mathrm {pod}$} function",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2249--2259",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005064",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005064",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{ElBachraoui:2011:IFS,
  author =       "Mohamed {El Bachraoui}",
  title =        "Inductive Formulas for Some Arithmetic Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2261--2268",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S179304211100509X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211100509X",
  abstract =     "We prove recursive formulas involving sums of divisors
                 and sums of triangular numbers and give a variety of
                 identities relating arithmetic functions to divisor
                 functions providing inductive identities for such
                 arithmetic functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Graves:2011:NPE,
  author =       "Hester Graves",
  title =        "Has a Non-Principal {Euclidean} Ideal",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2269--2271",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111004988",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111004988",
  abstract =     "This paper introduces a totally real quartic number
                 field with a non-principal Euclidean ideal.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kim:2011:AVM,
  author =       "Min-Soo Kim and Su Hu",
  title =        "A $p$-adic view of multiple sums of powers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2273--2288",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005027",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005027",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Anonymous:2011:AIV,
  author =       "Anonymous",
  title =        "Author Index (Volume 7)",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "7",
  number =       "8",
  pages =        "2289--2295",
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1142/S1793042111005118",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042111005118",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{FreixasIMontplet:2012:JLC,
  author =       "Gerard {Freixas I.Montplet}",
  title =        "The {Jacquet--Langlands} Correspondence and the
                 Arithmetic {Riemann--Roch} Theorem for Pointed Curves",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "1--29",
  month =        feb,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S1793042112500017",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500017",
  abstract =     "We show how the Jacquet--Langlands correspondence and
                 the arithmetic Riemann--Roch theorem for pointed
                 curves, relate the arithmetic self-intersection numbers
                 of the sheaves of modular forms with their Petersson
                 norms --- on modular and Shimura curves: these are
                 equal modulo $ \sum_{l \in S} $ {$ \mathbb {Q} $} log
                 l, where S is a controlled set of primes. These
                 quantities were previously considered by Bost and
                 K{\"u}hn (modular curve case) and Kudla--Rapoport--Yang
                 and Maillot--Roessler (Shimura curve case). By the work
                 of Maillot and Roessler, our result settles a question
                 raised by Soul{\'e}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Finotti:2012:NPC,
  author =       "Lu{\'i}s R. A. Finotti",
  title =        "Nonexistence of Pseudo-Canonical Liftings",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "31--51",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500029",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500029",
  abstract =     "In this paper we show that pseudo-canonical liftings
                 do not exist, by showing that if j$_0$ \mapsto (j$_0$,
                 J$_1$ (j$_0$), J$_2$ (j$_0$),\ldots) is the map that
                 gives canonical liftings for ordinary j$_0$, then J$_2$
                 has a pole at j$_0$ = 1728 if p \equiv 3 (mod 4) and
                 J$_3$ has a pole at j$_0$ = 0 if p \equiv 5 (mod 6).
                 Moreover, precise descriptions of J$_2$ and J$_3$ are
                 given.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Akbary:2012:GVT,
  author =       "Amir Akbary and Dragos Ghioca",
  title =        "A Geometric Variant of {Titchmarsh} Divisor Problem",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "53--69",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500030",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500030",
  abstract =     "We formulate a geometric analog of the Titchmarsh
                 divisor problem in the context of abelian varieties.
                 For any abelian variety A defined over {$ \mathbb {Q}
                 $}, we study the asymptotic distribution of the primes
                 of {\mathbb{Z}} which split completely in the division
                 fields of A. For all abelian varieties which contain an
                 elliptic curve we establish an asymptotic formula for
                 such primes under the assumption of Generalized Riemann
                 Hypothesis. We explain how to derive an unconditional
                 asymptotic formula in the case that the abelian variety
                 is a complex multiplication elliptic curve.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Amdeberhan:2012:II,
  author =       "Tewodros Amdeberhan and Christoph Koutschan and Victor
                 H. Moll and Eric S. Rowland",
  title =        "The iterated integrals of $ \ln (1 + x^n) $",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "71--94",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500042",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500042",
  abstract =     "For a polynomial P, we consider the sequence of
                 iterated integrals of ln P(x). This sequence is
                 expressed in terms of the zeros of P(x). In the special
                 case of ln(1 + x$^2$), arithmetic properties of certain
                 coefficients arising are described. Similar
                 observations are made for ln(1 + x$^3$).",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Castillo:2012:HOS,
  author =       "Daniel Macias Castillo",
  title =        "On higher-order {Stickelberger}-type theorems for
                 multi-quadratic extensions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "95--110",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500054",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500054",
  abstract =     "We prove, for all quadratic and a wide range of
                 multi-quadratic extensions of global fields, a result
                 concerning the annihilation as Galois modules of ideal
                 class groups by explicit elements constructed from the
                 values of higher-order derivatives of Dirichlet
                 {$L$}-functions. This result simultaneously refines
                 Rubin's integral version of Stark's Conjecture and
                 provides evidence for the relevant case of the
                 Equivariant Tamagawa Number Conjecture of Burns and
                 Flach.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Chan:2012:TCA,
  author =       "Song Heng Chan and Renrong Mao",
  title =        "Two Congruences for {Appell--Lerch} Sums",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "111--123",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500066",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500066",
  abstract =     "Two congruences are proved for an infinite family of
                 Appell--Lerch sums. As corollaries, special cases imply
                 congruences for some of the mock theta functions of
                 order two, six and eight.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Kadiri:2012:EZF,
  author =       "Habiba Kadiri",
  title =        "Explicit Zero-Free Regions for {Dedekind} Zeta
                 Functions",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "125--147",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500078",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500078",
  abstract =     "Let K be a number field, n$_K$ be its degree, and
                 d$_K$ be the absolute value of its discriminant. We
                 prove that, if d$_K$ is sufficiently large, then the
                 Dedekind zeta function \zeta$_K$ (s) has no zeros in
                 the region:, , where log M = 12.55 log d$_K$ +
                 9.69n$_K$ log|\Im {$ \mathfrak {m} $} s| + 3.03 n$_K$ +
                 58.63. Moreover, it has at most one zero in the
                 region:, . This zero if it exists is simple and is
                 real. This argument also improves a result of Stark by
                 a factor of 2: \zeta$_K$ (s) has at most one zero in
                 the region, .",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Schweiger:2012:DAR,
  author =       "F. Schweiger",
  title =        "A $2$-Dimensional Algorithm Related to the
                 {Farey--Brocot} Sequence",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "149--160",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S179304211250008X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211250008X",
  abstract =     "Moshchevitin and Vielhaber gave an interesting
                 generalization of the Farey--Brocot sequence for
                 dimension d \geq 2 (see [N. Moshchevitin and M.
                 Vielhaber, Moments for generalized Farey--Brocot
                 partitions, {\em Funct. Approx. Comment. Math.\/} 38
                 (2008), part 2, 131--157]). For dimension d = 2 they
                 investigate two special cases called algorithm and
                 algorithm. Algorithm is related to a proposal of
                 M{\"o}nkemeyer and to Selmer algorithm (see [G. Panti,
                 Multidimensional continued fractions and a Minkowski
                 function, {\em Monatsh. Math.\/} 154 (2008) 247--264]).
                 However, algorithm seems to be related to a new type of
                 2-dimensional continued fractions. The content of this
                 paper is first to describe such an algorithm and to
                 give some of its ergodic properties. In the second part
                 the dual algorithm is considered which behaves similar
                 to the Parry--Daniels map.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Filaseta:2012:S,
  author =       "M. Filaseta and S. Laishram and N. Saradha",
  title =        "Solving $ n (n + d) \cdots (n + (k - 1) d) = b y^2 $
                 with {$ P(b) \leq C k $}",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "161--173",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500091",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500091",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Noble:2012:AWD,
  author =       "Rob Noble",
  title =        "Asymptotics of the Weighted {Delannoy} Numbers",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "175--188",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S1793042112500108",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042112500108",
  abstract =     "The weighted Delannoy numbers give a weighted count of
                 lattice paths starting at the origin and using only
                 minimal east, north and northeast steps. Full
                 asymptotic expansions exist for various diagonals of
                 the weighted Delannoy numbers. In the particular case
                 of the central weighted Delannoy numbers, certain
                 weights give rise to asymptotic coefficients that lie
                 in a number field. In this paper we apply a
                 generalization of a method of Stoll and Haible to
                 obtain divisibility properties for the asymptotic
                 coefficients in this case. We also provide a similar
                 result for a special case of the diagonal with slope
                 2.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Fukshansky:2012:WRI,
  author =       "Lenny Fukshansky and Kathleen Petersen",
  title =        "On Well-Rounded Ideal Lattices",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "1",
  pages =        "189--206",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1142/S179304211250011X",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  bibdate =      "Tue Jul 21 10:01:27 MDT 2020",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S179304211250011X",
  abstract =     "We investigate a connection between two important
                 classes of Euclidean lattices: well-rounded a