arXiv Analytics

Sign in

arXiv:1511.07298 [math.NT]AbstractReferencesReviewsResources

On the distribution of Hecke eigenvalues for cuspidal automorphic representations for GL(2)

Nahid Walji

Published 2015-11-23Version 1

Given a self-dual cuspidal automorphic representation for GL(2) over a number field, we establish the existence of an infinite number of Hecke eigenvalues that are greater than an explicit positive constant, and an infinite number of Hecke eigenvalues that are less than an explicit negative constant. This provides an answer to a question of Serre. We also consider analogous problems for cuspidal automorphic representations that are not self-dual.

Comments: 12 pages. Comments welcome
Categories: math.NT
Related articles: Most relevant | Search more
arXiv:1404.0399 [math.NT] (Published 2014-04-01, updated 2014-11-29)
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average
arXiv:math/0302277 [math.NT] (Published 2003-02-22, updated 2004-01-10)
On the distribution of matrix elements for the quantum cat map
arXiv:1301.3232 [math.NT] (Published 2013-01-15)
Gaps between zeros of $ζ(s)$ and the distribution of zeros of $ζ'(s)$

Links

Toolbox