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arXiv:1609.06740 [math.NT]AbstractReferencesReviewsResources

Density Theorems for Exceptional Eigenvalues for Congruence Subgroups

Peter Humphries

Published 2016-09-21Version 1

Using the Kuznetsov formula, we prove several density theorems for exceptional Hecke and Laplacian eigenvalues of Maass cusp forms of weight 0 or 1 for the congruence subgroups $\Gamma_0(q)$, $\Gamma_1(q)$, and $\Gamma(q)$. These improve and extend upon results of Sarnak and Huxley, who prove similar but slightly weaker results via the Selberg trace formula.

Comments: 20 pages
Categories: math.NT
Subjects: 11F72, 11F30
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