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On signs of Fourier coefficients of cusp forms

Published online by Cambridge University Press:  05 December 2011

KAISA MATOMÄKI
KAISA MATOMÄKI*
Affiliation:
Department of Mathematics, University of Turku, 20014 Turku, Finland. e-mail: [email protected]
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Abstract

We consider two problems concerning signs of Fourier coefficients of classical modular forms, or equivalently Hecke eigenvalues: first, we give an upper bound for the size of the first sign-change of Hecke eigenvalues in terms of conductor and weight; second, we investigate to what extent the signs of Fourier coefficients determine an unique modular form. In both cases we improve recent results of Kowalski, Lau, Soundararajan and Wu. A part of the paper is also devoted to generalized rearrangement inequalities which are utilized in an alternative treatment of the second question.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 2 , March 2012 , pp. 207 - 222
Copyright
Copyright © Cambridge Philosophical Society 2011

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