Density theorems for GL(n)

Valentin Blomer

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arXiv · 1906.07459

Density theorems for GL(n)

Valentin Blomer

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Abstract

Strong bounds - going beyond Sarnak's density hypothesis - are obtained for the number of automorphic forms for the congruence subgroup Gamma_0(q) of SL_n(Z) violating the Ramanujan conjecture at any given unramified place. The proof is based on a relative trace formula of Kuznetsov type and best-possible bounds for certain Kloosterman sums for GL(n). Further applications are given.

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Valentin Blomer. 2019-06-18. Density theorems for GL(n). https://arxiv.org/abs/1906.07459

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