p-adic L-functions for Siegel modular forms

Location: ENR 2 S395
Series: Algebra and Number Theory Seminar Presenter: Zheng Liu, McGill

After introducing what p-adic L-functions are and why they are interesting objects, I explain how to construct the p-adic standard L-functions for Siegel modular forms (and their Hida families) using the doubling method, especially the strategy for choosing the local sections of the Siegel Eisenstein series on the doubling group. Such a choice allows p-adic interpolation and guarantees nonvanishing of the archimedean zeta integrals, and the corresponding local zeta integrals at p give the modified Euler factors at p as predicted by Coates for p-adic L-functions.