Achimedean period relations and period relations of automorphic L-functions

：孙斌勇（浙江大学）
：2023-05-09 10:00
：厦大海韵园实验楼105报告厅

报告人：孙斌勇（浙江大学）

时  间：2023年5月9日上午10:00-12:00

地  点：厦大海韵园实验楼105报告厅

内容摘要:

It was known to Euler that ζ(2k) is a rational multiple of π^2k, where ζ is the Euler-Riemann zeta function, and k is a positive integer. Following the pioneering works of G. Shimura, P. Deligne and etc., D. Blasius proposed a conjecture which asserts that similar rationality results hold for very general automorphic L-functions. We confirm Blasius’s conjecture in two cases: the standard L-functions of symplectic type (joint with Dihua Jiang and Fangyang Tian), and the Rankin-Selberg L-functions for GL(n)xGL(n-1) (joint with Jian-Shu Li and Dongwen Liu). The key ingredient is the Archimedean period relations for the modular symbols at infinity. These two cases have already been studied by many authors, including Harris-Lin, Grobner-Raghuram, Harder-Raghuram, Januszewski, Grobner-Lin, etc.

个人简介：

孙斌勇院士，于2004年获得香港科技大学博士学位，随后在中国科学院数学与系统科学研究院工作至2020年，现为浙江大学数学高等研究院教授。孙斌勇院士主要致力于典型群无穷维表示论、L-函数、以及它们之间联系等理论中基本问题的研究，取得了系统性的重要成果。他证明了这些领域中许多长期悬而未解的猜想，包括典型群的重数一猜想、Howe对偶猜想、Kudla-Rallis守恒律猜想,  Kazhdan-Mazur非零假设等。部分结果发表在Ann. Math., Journal of AMS, Invent. Math. 等数学重要期刊上。

 

联系人：陈福林