数论与表示论讨论班—— L-functions for Automorphic Forms on Classical Groups

Abstract:

The main problem concerned in this talk is the algebraicity of special L-values for automorphic forms on classical groups (Deligne's conjecture). After reviewing this problem, we will present an integral representation for L-functions by the doubling method. Using the integral representation and the Fourier expansion of Eisenstein series, we can prove the algebraicity result in the `holomorphic' case. We will also explain our future plan on studying this problem in full generality.