Research
Research in Number Theory 2016 2:33
Published on: 25 November 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
Research
Research in Number Theory 2016 2:15
Published on: 1 August 2016
Research
Research in Number Theory 2016 2:13
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
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
Research in Number Theory 2016 2:7
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