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On modular signs

Published online by Cambridge University Press:  19 July 2010

E. KOWALSKI ,
Y.-K. LAU ,
K. SOUNDARARAJAN  and
J. WU
E. KOWALSKI
Affiliation:
ETH Zürich – D-MATH, Rämistrasse 101, 8092 Zürich, Switzerland. e-mail: kowalski@math.ethz.ch
Y.-K. LAU
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong. e-mail: yklau@maths.hku.hk
K. SOUNDARARAJAN
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A. e-mail: ksound@stanford.edu
J. WU
Affiliation:
Institut Elie Cartan, Nancy-Université, INRIA, Boulevard des Aiguillettes, B.P. 239, 54506 Vandœuvre-lès-Nancy, France. e-mail: wujie@iecn.u-nancy.fr
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Abstract

We consider some questions related to the signs of Hecke eigenvalues or Fourier coefficients of classical modular forms. One problem is to determine to what extent those signs, for suitable sets of primes, determine uniquely the modular form, and we give both individual and statistical results. The second problem, which has been considered by a number of authors, is to determine the size, in terms of the conductor and weight, of the first sign-change of Hecke eigenvalues. Here we improve the recent estimate of Iwaniec, Kohnen and Sengupta.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 3 , November 2010 , pp. 389 - 411
Copyright
Copyright © Cambridge Philosophical Society 2010

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