Research
Research in Number Theory 2016 2:23
Published on: 10 October 2016
Research
Research in Number Theory 2016 2:23
Published on: 10 October 2016
Research
Research in Number Theory 2016 2:30
Published on: 5 October 2016
Research Article
Research in Number Theory 2016 2:29
Published on: 4 October 2016
Research
Research in Number Theory 2016 2:19
Published on: 3 October 2016
Research
We give a new proof of Serre’s result that a Noetherian local ring is regular if and only if it has finite global dimension. Our proof avoids the explicit construction of a Koszul complex.
Research in Number Theory 2016 2:18
Published on: 12 September 2016
Research
Given a formula for the Mahler measure of a rational function expressed in terms of polylogarithms, we describe a new method that allows us to construct a rational function with 2 more variables and whose Mahl...
Research in Number Theory 2016 2:17
Published on: 1 September 2016
Research
Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal ...
Research in Number Theory 2016 2:16
Published on: 8 August 2016
Research
In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta–theta functions by constructing mock modular forms from the eta–theta functions with even character...
Research in Number Theory 2016 2:14
Published on: 8 August 2016
Research
Research in Number Theory 2016 2:13
Published on: 1 August 2016
Research
Research in Number Theory 2016 2:15
Published on: 1 August 2016
Research
Research in Number Theory 2016 2:12
Published on: 11 July 2016
Research
Research in Number Theory 2016 2:11
Published on: 5 July 2016
Research
Let d≥1 be fixed. Let F be a number field of degree d, and let E/F be an elliptic curve. Let E(F)_{tors} be the torsion subgroup of E(F). In 1996, Merel proved the uniform boundedness conjecture, i.e., there is a co...
Research in Number Theory 2016 2:8
Published on: 15 April 2016
Research
We exploit transformations relating generalized q-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as
Research in Number Theory 2016 2:9
Published on: 15 March 2016
Research
Research in Number Theory 2016 2:7
Published on: 14 March 2016
Research
We study the distribution of rational points of bounded height on a one-sided equivariant compactification of PGL_{2} using automorphic representation theory of PGL_{2}.
Research in Number Theory 2016 2:6
Published on: 14 March 2016
Research
The smallest part is a rational function. This result is similar to the closely related case of partitions with fixed differences between largest and smallest parts which has recently been studied through anal...
Research in Number Theory 2016 2:2
Published on: 1 March 2016
Research
We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the f...
Research in Number Theory 2016 2:10
Published on: 15 February 2016
Research
Research in Number Theory 2016 2:1
Published on: 15 February 2016
Research
Research in Number Theory 2016 2:4
Published on: 14 February 2016
Research
In 1982, Gessel showed that the Apéry numbers associated to the irrationality of ζ(3) satisfy Lucas congruences. Our main result is to prove corresponding congruences for all known sporadic Apéry-like sequences. ...
Research in Number Theory 2016 2:5
Published on: 14 February 2016
Research
Research in Number Theory 2016 2:3
Published on: 20 January 2016
Research
Research in Number Theory 2015 1:28
Published on: 29 December 2015
Research Article
We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical ...
Research in Number Theory 2015 1:25
Published on: 21 December 2015
Research
A interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two ...
Research in Number Theory 2015 1:27
Published on: 21 December 2015