A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On signs of Fourier coefficients of cusp forms
Tekijät: Matomaki K
Kustantaja: CAMBRIDGE UNIV PRESS
Julkaisuvuosi: 2012
Lehti: Mathematical Proceedings of the Cambridge Philosophical Society
Tietokannassa oleva lehden nimi: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Lehden akronyymi: MATH PROC CAMBRIDGE
Vuosikerta: 152
Aloitussivu: 207
Lopetussivu: 222
Sivujen määrä: 16
ISSN: 0305-0041
DOI: https://doi.org/10.1017/S030500411100034X
Tiivistelmä
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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