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ON SIGN CHANGES FOR ALMOST PRIME COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  06 May 2016

Srilakshmi Krishnamoorthy  and
M. Ram Murty
Srilakshmi Krishnamoorthy
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India email srilakshmi@iitm.ac.in
M. Ram Murty
Affiliation:
Department of Mathematics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada email murty@mast.queensu.ca
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Abstract

For a half-integral weight modular form $f=\sum _{n=1}^{\infty }a_{f}(n)n^{(k-1)/2}q^{n}$ of weight $k=\ell +1/2$ on $\unicode[STIX]{x1D6E4}_{0}(4)$ such that $a_{f}(n)$ ( $n\in \mathbb{N}$ ) are real, we prove for a fixed suitable natural number $r$ that $a_{f}(n)$ changes sign infinitely often as $n$ varies over numbers having at most $r$ prime factors, assuming the analog of the Ramanujan conjecture for Fourier coefficients of half-integral weight forms.

MSC classification

Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F11: Holomorphic modular forms of integral weight
Secondary: 11F30: Fourier coefficients of automorphic forms
Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 801 - 810
Copyright
Copyright © University College London 2016 

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