On the fine expansion of the unipotent contribution of the Guo–Jacquet trace formula

Pierre-Henri Chaudouard

Vol. 305 (2020), No. 2, 539–561

DOI: 10.2140/pjm.2020.305.539

Abstract

For a useful class of functions (containing functions whose one finite component is essentially a matrix coefficient of a supercuspidal representation), we establish three results about the unipotent contribution of the Guo–Jacquet relative trace formula for the pair $\left({GL}_n\left(D\right),{GL}_n\left(E\right)\right)$. First we get a fine expansion in terms of global nilpotent integrals. Second we express these nilpotent integrals in terms of zeta integrals. Finally we prove that they satisfy certain homogeneity properties. The proof is based on a new kind of truncation introduced in a previous article.

Keywords

Guo–Jacquet trace formula, relative trace formula, unipotent contribution, orbital integrals, distinction problems, periods, automorphic forms

Mathematical Subject Classification 2010

Primary: 11F70

Milestones

Received: 23 August 2019

Revised: 25 October 2019

Accepted: 23 November 2019

Published: 29 April 2020