Absolute convergence of the twisted Arthur-Selberg trace formula
arXiv:1710.08885 · doi:10.1007/s00209-019-02290-0
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 Müller, 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.
Accepted to be published in Mathematische Zeitschrift. Removed proof of RCL for base change; Section 8 now requires Assumption 8.1. Also, minor corrections