Sur certaines contributions unipotentes dans la formule des traces d'Arthur

TL;DR

This paper proves a detailed expansion of the geometric part of Arthur's trace formula, specifically for general linear groups, providing explicit formulas for contributions of certain unipotent orbits and their associated global coefficients.

Contribution

It introduces a precise expansion of the geometric side of the trace formula and derives explicit formulas for contributions of unipotent orbits with one Jordan block in GL(n).

Findings

Established a fine expansion for the geometric part of the trace formula.

Derived explicit formulas for Arthur's global coefficients for specific unipotent orbits.

Confirmed conjectures related to unipotent contributions in the trace formula.

Abstract

We establish a fine expansion for the geometric part of the Arthur-Selberg trace formula (as it was conjectured by Werner Hoffmann). For the general linear group, we deduce an expression for the contributions of regular by blocks unipotent orbits (orbits with one Jordan block with multiplicity). As a consequence, we find formulas for Arthur's global coefficients attached to such orbits.