An orthogonality relation for a thin family of $GL(3)$ Maass forms

TL;DR

This paper establishes an orthogonality relation for Fourier-Whittaker coefficients of a specific thin family of $GL(3)$ Maass forms, using the Kuznetsov trace formula, and derives Weyl's law for this family.

Contribution

It introduces a new orthogonality relation for a thin family of $GL(3)$ Maass forms and applies the Kuznetsov trace formula to analyze their spectral properties.

Findings

Orthogonality relation for Fourier-Whittaker coefficients

Weyl's law for the specified family of Maass forms

Analysis of the Kuznetsov trace formula on $GL(3)$

Abstract

We prove an orthogonality relation for the Fourier-Whittaker coefficients of a thin family of $GL(3)$ Maass forms containing all self-dual forms. This is obtained by analysing the Kuznetsov trace formula on $GL(3)$ for a certain family of test functions. The method also yields Weyl's law for the same family of Maass forms.