Density theorems for GL(n)
Abstract
Strong bounds - going beyond Sarnak's density hypothesis - are obtained for the number of automorphic forms for the congruence subgroup Gamma0(q) of SLn(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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