An improved spectral large sieve inequality for $SL_3(\mathbb{Z})$

TL;DR

This paper establishes a stronger spectral large sieve inequality for $SL_3(\

Contribution

It introduces an improved inequality for $SL_3(\

Findings

Enhanced bounds for spectral large sieve for $SL_3(\

Connections to Heath-Brown's large sieve for cubic characters are revealed.

Abstract

We prove an improved spectral large sieve inequality for the family of $SL_3(\mathbb{Z})$ Hecke-Maass cusp forms. The method of proof uses duality and its structure reveals unexpected connections to Heath-Brown's large sieve for cubic characters.