Sign changes of coefficients of half integral weight modular forms

DOI10.1017/CBO9780511543371.005zbMATH Open1228.11061arXiv0709.2001OpenAlexW2968110182MaRDI QIDQ3596831

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Publication date: 9 February 2009

Published in: (Search for Journal in Brave)

Abstract: For a half integral weight modular form $f$ we study the signs of the Fourier coefficients $a(n)$. If $f$ is a Hecke eigenform of level $N$ with real Nebentypus character, and $t$ is a fixed square-free positive integer with $a(t)eq0$, we show that for all but finitely many primes $p$ the sequence $(a(t{p}^{2m}){)}_m$ has infinitely many signs changes. Moreover, we prove similar (partly conditional) results for arbitrary cusp forms $f$ which are not necessarily Hecke eigenforms.

Full work available at URL: https://arxiv.org/abs/0709.2001

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