On signs of Fourier coefficients of cusp forms



: Matomaki K

Publisher: CAMBRIDGE UNIV PRESS

: 2012

: Mathematical Proceedings of the Cambridge Philosophical Society

: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

: MATH PROC CAMBRIDGE

: 152

: 207

: 222

: 16

: 0305-0041

DOI: https://doi.org/10.1017/S030500411100034X


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.



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