Vol. 305, No. 2, 2020

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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

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 (GLn(D),GLn(E)). 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.

Guo–Jacquet trace formula, relative trace formula, unipotent contribution, orbital integrals, distinction problems, periods, automorphic forms
Mathematical Subject Classification 2010
Primary: 11F70
Received: 23 August 2019
Revised: 25 October 2019
Accepted: 23 November 2019
Published: 29 April 2020
Pierre-Henri Chaudouard
Université de Paris
Institut de Mathématiques de Jussieu - Paris Rive Gauche
F-75013 Paris