Plancherel distribution of Satake parameters of Maass cusp forms on $GL_3$

TL;DR

This paper establishes the equidistribution of Satake parameters for Maass cusp forms on GL_3 using the Kuznetsov trace formula, advancing understanding of automorphic forms and their distributions.

Contribution

It introduces methods to remove arithmetic weights in the Kuznetsov trace formula for GL_3, enabling new equidistribution results for Satake parameters.

Findings

Proves equidistribution of Satake parameters with respect to the p-adic Plancherel measure

Develops techniques to handle removal of arithmetic weights in trace formulas on GL_3

Enhances understanding of automorphic form distributions on higher rank groups

Abstract

We prove an equidistribution result for the Satake parameters of Maass cusp forms on $GL_3$ with respect to the $p$-adic Plancherel measure by using an application of the Kuznetsov trace formula. The techniques developed in this paper deal with the removal of arithmetic weight $L(1,F,Ad)^{-1}$ in the Kuznetsov trace formula on $GL_3$.