Global decomposition of GL(3) Kloosterman sums and the spectral large sieve

TL;DR

This paper establishes optimal bounds for bilinear forms in GL(3) Kloosterman sums and applies these results to derive the strongest possible spectral large sieve inequality for GL(3).

Contribution

It provides the first sharp bounds for bilinear forms in GL(3) Kloosterman sums and introduces a best-possible spectral large sieve inequality for GL(3).

Findings

Proved optimal bounds for bilinear forms in GL(3) Kloosterman sums.

Derived the strongest spectral large sieve inequality for GL(3).

Advances understanding of automorphic forms and exponential sums on GL(3).

Abstract

We prove best-possible bounds for bilinear forms in Kloosterman sums for GL(3) associated with the long Weyl element. As an application we derive a best-possible spectral large sieve inequality on GL(3).