Large Fourier coefficients of half-integer weight modular forms

Gun, S ; Kohnen, W ; Soundararajan, K (2020) Large Fourier coefficients of half-integer weight modular forms arXiv preprint arXiv:2004.14450 . pp. 1-20.

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Official URL: https://arxiv.org/pdf/2004.14450.pdf

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 D such that the Fourier coefficients evaluated at D are non-zero. By adapting the resonance method, we also demonstrate that such Fourier coefficients must take quite large values.

Item Type:Article
Keywords:Square-Free Fourier Coefficients Of Half-Integer Weight Cusp Forms; L-functions, Omega Result.
ID Code:117984
Deposited On:07 May 2021 12:03
Last Modified:07 May 2021 12:03

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