The number of Hecke eigenvalues of same signs

2008/12/16 by Lau, Yuk Kam, Wu, Jie
#11F30 #11N25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0812.3025

Abstract

We give the best possible lower bounds in order of magnitude for the number of positive and negative Hecke eigenvalues. This improves upon a recent work of Kohnen, Lau & Shparlinski. Also, we study an analogous problem for short intervals.

Related

• Bounds on the multiplicity of the Hecke eigenvalues
• On the average least negative Hecke eigenvalue
• Sign changes of Hecke eigenvalues
• Hecke Eigenforms as Products of Eigenforms
• Vanishing Fourier Coefficients of Hecke Eigenforms