Divisibility properties of coefficients of modular functions in genus zero levels
Number Theory
2018-07-30 v2
Abstract
We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight and levels with poles only at the cusp at infinity. In addition, we show that these Fourier coefficients satisfy Zagier duality in all weights, and give a general formula for the generating functions of such canonical bases for all genus zero levels.
Keywords
Cite
@article{arxiv.1711.06239,
title = {Divisibility properties of coefficients of modular functions in genus zero levels},
author = {Victoria Iba and Paul Jenkins and Merrill Warnick},
journal= {arXiv preprint arXiv:1711.06239},
year = {2018}
}