Bilinear forms with $GL_3$ Kloosterman sums and the spectral large sieve

TL;DR

This paper studies bilinear forms involving $GL_3$ Kloosterman sums and uses these results to improve bounds on the $GL_3$ spectral large sieve inequality, advancing understanding in analytic number theory.

Contribution

It introduces new bounds for bilinear forms with $GL_3$ Kloosterman sums and enhances the spectral large sieve estimates for $GL_3$.

Findings

Improved estimate for the $GL_3$ spectral large sieve inequality.

New bounds for bilinear forms involving $GL_3$ Kloosterman sums.

Enhanced techniques for analyzing automorphic forms and exponential sums.

Abstract

We analyze certain bilinear forms involving $GL_3$ Kloosterman sums. As an application, we obtain an improved estimate for the $GL_3$ spectral large sieve inequality.