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arXiv · 1007.4732

Prime density results for Hecke eigenvalues of a Siegel cusp form

Abhishek Saha
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Abstract

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.

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Abhishek Saha. 2010-07-27. Prime density results for Hecke eigenvalues of a Siegel cusp form. https://arxiv.org/abs/1007.4732

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