Density theorems for GL(n)

2019/06/18 by Blomer, Valentin · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1906.07459

Abstract

Strong bounds - going beyond Sarnak's density hypothesis - are obtained for the number of automorphic forms for the congruence subgroup Gamma₀(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.

Cited by

• Large sieves for GL_n and applications

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• Density theorems for GL_n via Rankin-Selberg L-functions
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• Bounds for Kloosterman sums on GL(n)
• A density theorem for Borel-Type Congruence subgroups and arithmetic applications