Density theorems for GL(n)
Number Theory
2022-11-11 v2
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.
Cite
@article{arxiv.1906.07459,
title = {Density theorems for GL(n)},
author = {Valentin Blomer},
journal= {arXiv preprint arXiv:1906.07459},
year = {2022}
}
Comments
Some updates and corrections. To appear in Invent. Math