Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	杨李扬博士，Princeton University
Inviter:
Title:	Relative Trace Formula and Arithmetic Applications
Language:	Chinese
Time & Venue:	2023.06.09 09:00-10:00 Zoom会议：825 6548 0902 密码：0609
Abstract:	In this talk, we will introduce a relative trace formula on $\mathrm{GL}(n+1)$ over number fields, incorporating cusp forms on $\mathrm{GL}(n)$. This formula combines the spectral side, involving average Rankin-Selberg L-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$across the entire spectrum, with the geometric side, consisting of Rankin-Selberg L-functions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$ and specific meromorphic functions. We provide a comprehensive description of the regularization process and emphasize thearithmetic implications of the relative trace formula, particularly in relation to central $L$-values.