Erratum
Research in Number Theory 2017 3:12
Published on: 10 February 2017
Erratum
Research in Number Theory 2017 3:12
Published on: 10 February 2017
Research
Research in Number Theory 2017 3:4
Published on: 1 February 2017
Research
We study the variance of sums of the indicator function of square-full polynomials in both arithmetic progressions and short intervals. Our work is in the context of the ring ...
Research in Number Theory 2017 3:3
Published on: 17 January 2017
Research
We prove an explicit formula for the polynomial part of a restricted partition function, also known as the first Sylvester wave. This is achieved by way of some identities for higher-order Bernoulli polynomial...
Research in Number Theory 2017 3:1
Published on: 5 January 2017
Research
Research in Number Theory 2016 2:34
Published on: 14 December 2016
Research
We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to Dèbes and Emsalem can be used to prove this statement in the...
Research in Number Theory 2016 2:27
Published on: 13 December 2016
Research
We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduce a rank-like function, estab...
Research in Number Theory 2016 2:35
Published on: 13 December 2016
Research
In a recent paper, Bacher and de la Harpe study the conjugacy growth series of finitary permutation groups. In the course of studying the coefficients of a series related to the finitary alternating group, the...
Research in Number Theory 2016 2:20
Published on: 12 December 2016
Research
Feng and Wu introduced a new general coefficient sequence into Montgomery and Odlyzko’s method for exhibiting irregularity in the gaps between consecutive zeros of ...
Research in Number Theory 2016 2:28
Published on: 8 December 2016
Research
Research in Number Theory 2016 2:33
Published on: 25 November 2016
Research
The mock theta conjectures are ten identities involving Ramanujan’s fifth-order mock theta functions. The conjectures were proven by Hickerson in 1988 using q-series methods. Using methods from the theory of harm...
Research in Number Theory 2016 2:32
Published on: 25 November 2016
Research
Let K be a composite field of some real quadratic fields. We give a sufficient condition on K such that all elliptic curves over K are modular.
Research in Number Theory 2016 2:31
Published on: 24 November 2016
Research
In this series we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper begi...
Research in Number Theory 2016 2:24
Published on: 21 November 2016
Research
In Pollack and Stevens (Ann Sci Éc Norm Supér 44(1):1–42, 2011), efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of p-adic L-fun...
Research in Number Theory 2016 2:25
Published on: 14 November 2016
Research
Research in Number Theory 2016 2:21
Published on: 1 November 2016
Research
We revisit the mathematics that Ramanujan developed in connection with the famous “taxi-cab” number 1729. A study of his writings reveals that he had been studying Euler’s diophantine equation
Research in Number Theory 2016 2:26
Published on: 17 October 2016
Research
Research in Number Theory 2016 2:23
Published on: 10 October 2016
Research
Research in Number Theory 2016 2:22
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
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
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