华罗庚青年数学论坛综合报告：Relative Trace Formula and Arithmetic Applications

中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 杨李扬 博士（Princeton University）

题  目：Relative Trace Formula  and Arithmetic Applications

时  间：2023.06.09（星期五），09:00-10:00

地  点：Zoom会议：825 6548 0902   密码：0609

摘  要：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.