P-Adic L-Functions for Finite-Slope Families on Symplectic and Unitary Groups
Shimura Varieties and L-Functions March 13, 2023 - March 17, 2023
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
We use the doubling method to construct p-adic L-functions for finite-slope families of automorphic forms on symplectic and unitary groups. A key construction is the p-adic deformation of iterations of Maass-Shimura differential operators on nearly overconvergent families. We will explain how to generalize the construction for GL(2) by Andreatta and Iovita, and how to bypass explicit computations of formulas of iterations of differential operators on q-expansions by using dynamics of U_p operators.