La formule des traces pour les rev\^etements de groupes r\'eductifs connexes. III. Le d\'eveloppement spectral fin

TL;DR

This paper advances the spectral analysis of Arthur's invariant trace formula for certain reductive group coverings, providing explicit formulas based on local harmonic analysis and fine-tuning of Arthur's methods.

Contribution

It extends Arthur's trace formula to specific group coverings, offering explicit spectral formulas and detailed adjustments for these cases.

Findings

Explicit spectral formulas for group coverings

Refined harmonic analysis techniques applied

Enhanced understanding of trace formula for coverings

Abstract

We pursue Arthur's invariant trace formula for certain coverings of connected reductive groups by deducing explicit formulas for its spectral side. This is based on some results in local harmonic analysis from an earlier preprint. The arguments are due to Arthur, and we will explain the necessary fine-tunings for coverings.