Absolute convergence of the twisted Arthur-Selberg trace formula

TL;DR

This paper proves the absolute convergence of the twisted Arthur-Selberg trace formula distributions for non-compact test functions, extending previous work and enabling new interpretations of Rankin-Selberg L-functions.

Contribution

It extends the absolute convergence results of the trace formula to the twisted case and non-compact test functions, building on prior work by Finis-Lapid and Müller.

Findings

Distributions extend to non-compactly supported test functions.

Absolute convergence enables geometric interpretation of L-function residues.

Results hold under certain root system hypotheses for split groups.

Abstract

We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven when the group is split. The result extends the work of Finis-Lapid (and M\"uller, spectral side) to the twisted setting. We use the absolute convergence to give a geometric interpretation of sums of residues of certain Rankin-Selberg L-functions.