中科院数学与系统科学研究院

数学研究所

数论研讨班

报告人：田昉旸 博士 (National University of Singapore)

题 目：Period Relations of Standard L-Functions of Symplectic Type

时 间：2021.01.21（星期四）, 16:00-17:00

地 点：数学院南楼N205

Zoom会议：677 5021 9154  密码：721145

摘 要：A classical result of Euler says that the value of the Riemann-Zeta function at a positive even integer $2k$ is a rational multiple of $\pi^{2k}$. This type of result, conjectured by D. Blasius for general linear groups, is called period relation of a certainautomorphic $L$-function, which is closely related to a celebrated conjecture of P. Deligne. In this talk, I will discuss my work joint with Dihua Jiang and Binyong Sun on the period relation for the twisted standard L-function $L(s, \Pi\otimes\chi)$, where $\Pi$ is an irreducible cuspidal automorphic representation of $GL_{2n}(\mathbb{A})$ which isregular algebraic and of symplectic type. Our result generalizes many predecessors' work, such as Ash-Ginzburg, Grobner-Raghuram, Januszewski, to mention a few.