#### 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
##### 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
Primary: 11F70