Bounds for global coefficients in Arthur’s fine expansion (general reductive groups)

Develop uniform bounds for the global coefficients appearing in Arthur’s fine expansion of the unipotent contribution to the trace formula for general reductive groups over number fields, beyond the GL(n)/F case where such bounds are available; these bounds are needed to establish approximation results for regularized analytic torsion via the trace formula.

Background

The authors use the Arthur trace formula framework to approximate L^2-analytic torsion by regularized analytic torsion. This requires bounds on certain global coefficients in the fine expansion of the unipotent part of the geometric side of the trace formula.

While Matz has obtained suitable bounds for GL(n)/F, the authors note that, in general, the existence of such bounds remains unresolved. Establishing these bounds broadly would extend techniques used in the paper to wider classes of groups.