Vol. 315, No. 1, 2021

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An infinitesimal variant of the Guo–Jacquet trace formula, II

Huajie Li

Vol. 315 (2021), No. 1, 151–207

We establish an infinitesimal variant of the Guo–Jacquet trace formula for the case of a central simple algebra over a number field F containing a quadratic field extension EF. It is an equality between a sum of geometric distributions on the tangent space of some symmetric space and its Fourier transform. To prove this, we need to define an analogue of Arthur’s truncation and then use the Poisson summation formula. We describe the terms attached to regular semisimple orbits as explicit weighted orbital integrals. To compare them to those for another case studied in our previous work, we state and prove the weighted fundamental lemma at the infinitesimal level by using Labesse’s work on the base change for GLn.

Guo–Jacquet trace formula, Arthur's truncation, weighted fundamental lemma
Mathematical Subject Classification
Primary: 11F70, 11F72, 20G35, 22E35
Received: 20 January 2020
Revised: 16 March 2021
Accepted: 2 September 2021
Published: 13 December 2021
Huajie Li
Aix-Marseille Université, CNRS, Institut de Mathématiques de Marseille