A1 Refereed original research article in a scientific journal
On signs of Fourier coefficients of cusp forms
Authors: Matomaki K
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2012
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
Journal name in source: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Journal acronym: MATH PROC CAMBRIDGE
Volume: 152
First page : 207
Last page: 222
Number of pages: 16
ISSN: 0305-0041
DOI: https://doi.org/10.1017/S030500411100034X
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.
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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