- BIMSA-YMSC 清华数论讨论班

Beyond Endoscopy via the Limit Form of the Trace Formula

组织者

刁晗生 , 杜衡 , 胡悦科 , ‌李华杰 , 徐斌 , 朱艺航

演讲者

程昱皓

时间

2026年05月25日 10:00 至 11:00

地点

Shuangqing-C654

摘要

Beyond endoscopy, suggested by Langlands, is an attempt to attack the general functoriality conjectures. It can be described as a two-step process. The first step is to identify, for a given reductive algebraic group, those automorphic representations that are functorial transfers from other groups. The second step is to compare this data for different groups. In order to isolate those representations, one considers the behavior of the automorphic $L$-functions at $s = 1$ for various finite dimensional representations of the dual group. Langlands proposed attacking this problem by a “limit form of the trace formula”. In this talk, I will establish asymptotic formulas for each term of the Arthur-Selberg trace formula when summing over $n \lt X$ for $GL(2)$ and the standard representation, up to an error of $o(X)$. This yields an identity depending on the parameter $X$, leading to certain identities that can be regarded as local and global limit forms of the trace formula for $GL(2)$.