Applications of the Kuznetsov formula on GL(3): the level aspect

Abstract

We develop an explicit Kuznetsov formula on GL(3) for congruence subgroups. Applications include a Lindelof on average type bound for the sixth moment of GL(3) L-functions in the level aspect, an automorphic large sieve inequality, density results for exceptional eigenvalues and density results for Maass forms violating the Ramanujan conjecture at finite places.