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arXiv · 1609.06740

Density Theorems for Exceptional Eigenvalues for Congruence Subgroups

Peter Humphries
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Abstract

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 $Γ_0(q)$, $Γ_1(q)$, and $Γ(q)$. These improve and extend upon results of Sarnak and Huxley, who prove similar but slightly weaker results via the Selberg trace formula.

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BibTeXRIS

Peter Humphries. 2018-11-03. Density Theorems for Exceptional Eigenvalues for Congruence Subgroups. https://doi.org/10.2140/ant.2018.12.1581

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