The trace formula and prehomogeneous vector spaces
Abstract
We describe an approach to express the geometric side of the Arthur-Selberg trace formula in terms of zeta integrals attached to prehomogeneous vector spaces. This will provide explicit formulas for weighted orbital integrals and for the coefficients by which they are multiplied in the trace formula. We implement this programme for the principal unipotent conjugacy class. The method relies on certain convergence results and uses the notions of induced conjugacy classes and canonical parabolic subgroups. So far, it works for certain types of conjugacy classes, which covers all classes appearing in classical groups of absolute rank up to two.
Cite
@article{arxiv.1412.8673,
title = {The trace formula and prehomogeneous vector spaces},
author = {Werner Hoffmann},
journal= {arXiv preprint arXiv:1412.8673},
year = {2014}
}
Comments
Submitted to the proceedings of the Simons Symposium "Families of Automorphic Forms and the Trace Formula", January 26 - February 1, 2014 in Rio Grande, Puerto Rico