Period Relations of Standard L-functions of Symplectic Type

Date: 2021-09-24 10:22:35
Time: 10:30-11:30
Venue: Yuquan Campus
Speaker: TIAN Fangyang
Category: Talk & Lecture

Speaker: TIAN Fangyang, Doctor of school of mathematic science, Zhejiang University

Venue: Room 200-9, Run Run Shaw Business Administration Building, Yuquan Campus


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 $\pi^{2k}$. In the 1970s, a successive pioneering work of G. Shimura revealed the relation of different critical values of $L$-function that are attached to modular forms of$\mathrm{GL}_2$. This type of result, conjectured by D. Blasius for general linear groups, is called period relation of a certain automorphic $L$-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 is regular algebraic and of symplectic type.  Along this talk, I will also discuss the key ingredient of this project - the existence of uniform cohomological test vector, which provides the most precise information on the archimedean local integrals.

Contact: LI Fang, fangli@zju.edu.cn