On the absolute convergence of the spectral side of the Arthur trace formula for GL(n)

TL;DR

This paper proves that the spectral side of the Arthur trace formula for GL(n) over a number field converges absolutely for all integrable rapidly decreasing functions, ensuring mathematical rigor in spectral analysis.

Contribution

It establishes the absolute convergence of the spectral side of the Arthur trace formula for GL(n), a key step in understanding automorphic representations.

Findings

Spectral side of trace formula is absolutely convergent.

Convergence holds for all integrable rapidly decreasing functions.

Supports further analysis of automorphic forms and representations.

Abstract

Let G be the group GL(n) over a number field E and let A be the ring of adeles of E. In this paper we prove that the spectral side of the Arthur trace formula for G is absolutely convergent for all integrable rapidly decreasing functions on $G(A)^1$.