Large Fourier coefficients of half-integer weight modular forms
Number Theory
2020-05-01 v1
Abstract
This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants such that the Fourier coefficients evaluated at are non-zero. By adapting the resonance method, we also demonstrate that such Fourier coefficients must take quite large values.
Cite
@article{arxiv.2004.14450,
title = {Large Fourier coefficients of half-integer weight modular forms},
author = {S. Gun and W. Kohnen and K. Soundararajan},
journal= {arXiv preprint arXiv:2004.14450},
year = {2020}
}