Geodesic
An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of $(\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})$
Documenta mathematica, Tome 27 (2022), pp. 315-381.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11F70, 11F72, 20G35
Keywords: Guo-Jacquet trace formula, Arthur's truncation 
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Li, Huajie. An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of \((\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})\). Documenta mathematica, Tome 27 (2022), pp. 315-381. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a59/