Computing p-adic L-functions of Hecke characters

11 October 2021
16:00
Håvard Damm-Johnsen
Abstract

In 1973, Serre defined $p$-adic modular forms as limits of modular forms, and constructed the Leopoldt-Kubota $L$-function as the constant term of a limit of Eisenstein series. This was extended by Deligne-Ribet to totally real number fields, and Lauder and Vonk have developed an algorithm for interpolating $p$-adic $L$-functions of such fields using Serre's idea. We explain what an $L$-function is and why you should care, and then move on to giving an overview of the algorithm, extensions, and applications.

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  • Junior Number Theory Seminar