Density theorems for GL(n)

DOI10.1007/S00222-022-01172-3arXiv1906.07459WikidataQ122416186 ScholiaQ122416186MaRDI QIDQ6320668

Publication date: 18 June 2019

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.

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

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