Beyond Endoscopy via the Limit Form of the Trace Formula

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu, Huajie Li

Speaker：

Yuhao Cheng 程昱皓（Tsinghua university）

Time：

Mon., 10:00-11:00 am, May 11, 2026

Venue：

C654, Shuangqing Complex Building A

Title：

Beyond Endoscopy via the Limit Form of the Trace Formula

Abstract:

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<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).