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arXiv:1007.4732 [math.NT]AbstractReferencesReviewsResources

Prime density results for Hecke eigenvalues of a Siegel cusp form

Abhishek Saha

Published 2010-07-27, updated 2010-07-30Version 2

Let F in S_k(Sp(2g, Z)) be a cuspidal Siegel eigenform of genus g with normalized Hecke eigenvalues mu_F(n). Suppose that the associated automorphic representation pi_F is locally tempered everywhere. For each c>0 we consider the set of primes p for which |mu_F(p)| >= c and we provide an explicit upper bound on the density of this set. In the case g=2, we also provide an explicit upper bound on the density of the set of primes p for which mu_F(p) >= c.

Comments: 8 pages. Minor changes made over previous version. To appear in Int. J. Number Theory
Categories: math.NT
Subjects: 11F46, 11F66, 11F70, 22E50
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