AQFT Lecture Series

Speaker: Dihua Jiang (U Minnesota)

Title: Shalika Periods: Functoriality and Arithmetic

Abstract: Shalika periods of automorphic forms were first used by H. Jacquet and J. Shalika (1990) in their construction of global zeta integrals for exterior square L-functions of GL(2n). They were also used by S. Friedberg and H. Jacquet (1993) in their construction of global zeta integrals for the standard L-functions with connections to the linear periods. A. Ash and D. Ginzburg (1994) used them in their study of p-adic L-functions of GL(2n). In this talk, we will first review the implication of the Shalika periods to the Langlands functoriality and the connections with automorphic descents and theta correspondence. Then we turn to my recent work joint with B. Sun and F. Tian on an application of Shalika periods to algebraicity of critical L-values of cuspidal automorphic of GL(2n) of symplectic type.