Results 11 to 20 of about 334 (46)
q-hypergeometric double sums as mock theta functions [PDF]
, 2012 Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews +5 more
core +3 more sources
On congruence equations arising from suborbital graphs [PDF]
, 2019 In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of Γ_0(m) in PSL(2,R) . We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations.
Beşenk, Murat +2 more
core +2 more sources
Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
core +1 more source
Modular equations of a continued fraction of order six
Open Mathematics, 2019 We study a continued fraction X(τ) of order six by using the modular function theory. We first prove the modularity of X(τ), and then we obtain the modular equation of X(τ) of level n for any positive integer n; this includes the result of Vasuki et al ...
Lee Yoonjin, Park Yoon Kyung
doaj +1 more source
On two 10th order mock theta identities
, 2013 We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan ...
A. Folsom +8 more
core +3 more sources
On three theorems of Folsom, Ono and Rhoades
, 2013 In his deathbed letter to Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom,
Zudilin, Wadim
core +1 more source
, 2012 We explain the use and set grounds about applicability of algebraic transformations of arithmetic hypergeometric series for proving Ramanujan's formulae for $1/\pi$ and their generalisations.Comment: 6 ...
Zudilin, Wadim
core +1 more source
A generating function of the squares of Legendre polynomials
, 2012 We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we
Zudilin, Wadim
core +1 more source
Equidistribution of signs for Hilbert modular forms of half-integral weight
, 2018 We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence.
Kaushik, Surjeet +2 more
core +1 more source
On the ramification of modular parametrizations at the cusps
, 2018 We investigate the ramification of modular parametrizations of elliptic curves over Q at the cusps. We prove that if the modular form associated to the elliptic curve has minimal level among its twists by Dirichlet characters, then the modular ...
Brunault, François
core +1 more source