Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms
Number Theory
2016-07-12 v2
Abstract
In this paper, we investigate Fourier expansions of meromorphic modular forms. Over the years, a number of special cases of meromorphic modular forms were shown to have Fourier expansions closely resembling the expansion of the reciprocal of the weight Eisenstein series which was computed by Hardy and Ramanujan. By investigating meromorphic modular forms within a larger space of so-called polar harmonic Maass forms, we prove in this paper that all negative-weight meromorphic modular forms (and furthermore all quasi-meromorpic modular forms) have Fourier expansions of this type, granted that they are bounded towards .
Keywords
Cite
@article{arxiv.1603.09250,
title = {Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms},
author = {Kathrin Bringmann and Ben Kane},
journal= {arXiv preprint arXiv:1603.09250},
year = {2016}
}