Applications of the Kuznetsov formula on GL(3)

TL;DR

This paper develops an explicit Kuznetsov formula on GL(3) and explores its applications to spectral theory, including Weyl's law, eigenvalues, sieve methods, and L-functions.

Contribution

It introduces a detailed Kuznetsov formula on GL(3) and analyzes test functions, enabling new applications in automorphic forms and number theory.

Findings

Derived an explicit Kuznetsov formula for GL(3)

Analyzed the analytic behavior of test functions

Applied the formula to Weyl's law, eigenvalues, sieve, and L-functions

Abstract

We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behaviour of the test functions on both sides. Applications to Weyl's law, exceptional eigenvalues, a large sieve and L-functions are given.