# An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of $(\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})$

### Huajie Li

Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany

## Abstract

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of $(GL_{2n, D}, GL_{n, D}\times GL_{n, D})$. It is a kind of Poisson summation formula obtained by an analogue of Arthur's truncation process. It consists in the equality of the sums of two types of distributions which are non-equivariant in general: one type is associated to rational points in the categorical quotient, while the other type is the Fourier transform of the first type. For regular semi-simple points in the categorical quotient, we obtain weighted orbital integrals.

## Cite this article

Huajie Li, An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of $(\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})$. Doc. Math. 27 (2022), pp. 315–381

DOI 10.4171/DM/872