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P-Adic L-Functions for Finite-Slope Families on Symplectic and Unitary Groups

Shimura Varieties and L-Functions March 13, 2023 - March 17, 2023

March 17, 2023 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Zheng Liu (University of California, Santa Barbara)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

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.

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