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SIGN OF FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF-INTEGRAL WEIGHT

Part of: Multiplicative number theory Zeta and $L$-functions: analytic theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  17 May 2016

Yuk-kam Lau ,
Emmanuel Royer  and
Jie Wu
Yuk-kam Lau
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong email [email protected]
Emmanuel Royer
Affiliation:
Université Clermont Auvergne, Université Blaise Pascal, Laboratoire de Mathématiques, BP 10448, F-63000 Clermont-Ferrand, France CNRS, UMR 6620, LM, F-63178 Aubière, France email [email protected]
Jie Wu
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China CNRS, Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, F-54506 Vandœuvre-lès-Nancy, France Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, F-54506 Vandœuvre-lès-Nancy, France email [email protected]
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Abstract

We establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke eigenform.

MSC classification

Primary: 11F30: Fourier coefficients of automorphic forms
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11M41: Other Dirichlet series and zeta functions 11N25: Distribution of integers with specified multiplicative constraints
Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 866 - 883
Copyright
Copyright © University College London 2016 

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