论文标题
GU-JACQUET痕量公式II的无限型变体
An infinitesimal variant of Guo-Jacquet trace formula II
论文作者
论文摘要
我们为中央简单代数$ f $的情况下建立了Guo-jacquet Trace公式的无限变体，其中包含二次场扩展$ e/f $。这是在某些对称空间的切线与其傅立叶变换的切线空间上的几何分布之和之间的平等性。为了证明这一点，我们需要定义亚瑟截断的类似物，然后使用泊松求和公式。我们将附加在常规半简单轨道上的术语描述为显式加权轨道积分。为了将它们与以前工作中研究的另一个案例进行比较，我们通过使用Labesse在$ GL_N $上使用Labesse在基本变更方面的工作来指出并证明无限级别的加权基本引理。
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 state and prove the weighted fundamental lemma at the infinitesimal level by using Labesse's work on the base change for $GL_n$.
