球簇上的相对迹公式方法  

The relative trace formula approach for spherical varieties

作　　者：蔡立 许宾[2] Li Cai;Bin Xu

机构地区：[1]清华大学丘成桐数学科学中心,北京100084 [2]四川大学数学学院,成都610064

出　　处：《中国科学：数学》2021年第10期1513-1536,共24页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11971254和11501382)资助项目。

摘　　要：本文给出关于整体域上球簇(spherical variety)的相对迹公式(relative trace formula)方法的一般框架,并且将其应用于Sakellaridis和Venkatesh提出的关于球簇上周期积分(period integral)的猜想.这一方法对于数论研究专家是熟知的但(至少对于我们而言)缺乏文献.本文的框架基于最近Beuzart-Plessis等(2019)引入的(对于数域的)分离谱技术,从而避免了直接进行精细谱展开的困难.该技术在函数域情形也可实现.We present a general framework for the relative trace formula approach to the conjecture of Sakellaridis and Venkatesh on period integrals for spherical varieties over global fields. This approach is somehow well-known for experts but it seems lack of literature. Our approach is based on the spectrum isolation technique developed by Beuzart-Plessis et al.(2019) for number fields, which avoids the difficulty from the refined spectral expansion. This technique is also available in the function field case.

关 键 词：球簇 相对迹公式 L-函数 周期积分 

分 类 号：O152[理学—数学]