Sign changes of a product of Dirichlet character and Fourier coefficients of half integral weight modular forms

2017/06/15 by Soufiane, Mezroui
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.05013

Abstract

Let f∈ S_k+1/2(N,χ) be a Hecke eigenform of half integral weight k+1/2 (k≥ 2) and the real nebentypus χ=± 1 where the Fourier coefficients a(n) are reals. We prove that the sequence \χ(p^ν)a(tp^2ν)\_ν∈\N has infinitely many sign changes for almost all primes p where t is a squarefree integer such that a(t)≠ 0. The same result holds for the sequences of Fourier coefficients \a(tp^2(2ν+1))\_ν∈\N and \a(tp^4ν)\_ν∈\N.

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• Sign changes of coefficients of half integral weight modular forms
• Sign changes of a product of Dirichlet characters and Fourier coefficients of Hecke eigenforms
• Sign changes of fourier coefficients of modular forms of half integral weight, 2
• Sign of Fourier coefficients of half-integral weight modular forms in arithmetic progressions
• Signs of Fourier coefficients of half-integral weight modular forms