Sign changes of coefficients of half integral weight modular forms

2007/09/13 by Jan Hendrik Bruinier, Winfried Kohnen, Bruinier, Jan Hendrik +1 · 2 citations
Mathematics · #11F30 #11F37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0709.2001

openalex publication_date 2007/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)≠ 0, we show that for all but finitely many primes p the sequence (a(tp^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.

Cited by

• Signs of Square-Free Fourier Coefficients of Half-Integral weight cusp forms and the Congruent Number Problem
• Selberg orthogonality for half-integral weight modular forms

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