Two-divisibility of the coefficients of certain weakly holomorphic modular forms
Number Theory
2013-05-15 v2
Abstract
We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.
Keywords
Cite
@article{arxiv.1105.0684,
title = {Two-divisibility of the coefficients of certain weakly holomorphic modular forms},
author = {Darrin Doud and Paul Jenkins and John Lopez},
journal= {arXiv preprint arXiv:1105.0684},
year = {2013}
}
Comments
Corrected typos. To appear in the Ramanujan Journal