On the fine expansion of the unipotent contribution of the Guo-Jacquet trace formula

关于某些傅里叶变换之间恒等式的研究：加uo-杰克特迹公式中加权轨道积分的微分对称空间

On certain identities between Fourier transforms of weighted orbital integrals on infinitesimal symmetric spaces of Guo-Jacquet

本文研究了加uo-杰克特迹公式中微分对称空间上加权轨道积分的傅里叶变换关系，探讨其在非不变比较中的应用。

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

We establish an invariant local trace formula for the tangent space of some symmetric spaces over a non-archimedean local field of characteristic zero. These symmetric spaces are studied in Guo-Jacquet trace formulae and our methods are inspired by works of Waldspurger and Arthur. Some other results are given during the proof including a noninvariant local trace formula, Howe's finiteness for weighted orbital integrals and the representability of the Fourier transform of weighted orbital integrals. These local results are prepared for the comparison of regular semi-simple terms, which are weig…

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

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.

An infinitesimal variant of Guo-Jacquet trace formula II

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of a central simple algebra over a number field $F$ containing a quadratic field extension $E/F$. 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 semi-simple orbits as explicit weighted orbital integrals. To compare them to those for another case studied in our previous work, we sta…

On the smooth transfer for Guo-Jacquet relative trace formulae

We establish the existence of smooth transfer for Guo-Jacquet relative trace formulae in $p$-adic case. This kind of smooth transfer is a key step towards a generalization of Waldspurger's result on central values of L-functions of $GL_2$.

对称空间的跟踪公式。Guo-Jacquet情况

Une formule des traces pour les espaces symétriques. Le cas de Guo-Jacquet

本文提出了一种对称空间的跟踪公式，用于研究自守谱和L函数特殊值之间的联系，通过谱分布与几何分布的恒等式，结合正则半简单数据和非正则数据的处理方法。