An infinitesimal variant of Guo-Jacquet trace formula I: the case of $(G{L}_{2n,D},G{L}_{n,D}\times G{L}_{n,D})$

Abstract

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of $(G{L}_{2n,D},G{L}_{n,D}\times G{L}_{n,D})$. 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.

42 pages; revision according to the referee report

References in corpus (3)

• Periods and nonvanishing of central L-values for GL(2n)
• On the smooth transfer for Guo-Jacquet relative trace formulae
• La variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes linéaires

Cited by in corpus (2)

• An infinitesimal variant of Guo-Jacquet trace formula II
• A local trace formula for $p$-adic infinitesimal symmetric spaces: the case of Guo-Jacquet