Speaker：Binyong Sun (Zhejiang University)

Time：2023-5-9, 10:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

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.