Shalika Periods: Functoriality and Arithmetic

Explore a 54-minute mathematics lecture from Harvard CMSA's AQFT series where Professor Dihua Jiang from the University of Minnesota examines Shalika periods in automorphic forms, their historical development, and modern applications. Begin with an overview of how Jacquet and Shalika first employed these periods in 1990 for constructing global zeta integrals for exterior square L-functions of GL(2n), followed by Friedberg and Jacquet's 1993 work connecting them to linear periods. Learn about Ash and Ginzburg's 1994 research applying Shalika periods to p-adic L-functions. Delve into the relationship between Shalika periods and Langlands functoriality, including connections to automorphic descents and theta correspondence. Conclude with recent developments from Jiang's collaborative research with Sun and Tian on using Shalika periods to study algebraicity of critical L-values in cuspidal automorphic forms of GL(2n) of symplectic type.