Density Theorems for Exceptional Eigenvalues for Congruence Subgroups

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 ${\Gamma }_0(q)$, ${\Gamma }_1(q)$, 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.

27 pages. Final version

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