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

TL;DR

This paper develops an explicit Kuznetsov formula on GL(3) for congruence subgroups and applies it to derive bounds, inequalities, and density results related to automorphic forms and L-functions in the level aspect.

Contribution

It introduces a new explicit Kuznetsov formula on GL(3) for congruence subgroups and demonstrates its applications to bounds and density results in automorphic forms.

Findings

Established a Lindelof on average bound for sixth moments of GL(3) L-functions

Derived an automorphic large sieve inequality

Provided density results for exceptional eigenvalues and Maass forms violating Ramanujan conjecture

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.