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BIMSA-YMSC Tsinghua Number Theory Seminar
BIMSA-YMSC Tsinghua Number Theory Seminar
Beyond Endoscopy via the Limit Form of the Trace Formula
Beyond Endoscopy via the Limit Form of the Trace Formula
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Huajie Li
, Bin Xu
, Yihang Zhu
Speaker
Yuhao Cheng
Time
Monday, May 25, 2026 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
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 $n \lt X$ 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 $GL(2)$.