Automorphic p-adic L-functions and regulators

Mini-course 1: Lecture 1 (Critical L-values)

16 oct. 2019, 11:00

1h

Salle de réunion (University of Lille)

Orateur

Andrei Jorza (University of Notre Dame)

Description

We recall general conjectures about the existence of $p$-adic $L$-functions attached to motives and automorphic representations. Then the lecture is devoted to the study of the critical values of the complex $L$-function of cuspidal automorphic representations of $\mathrm{GL}(2n)$ admitting a Shalika model. In particular we describe such $L$-values in terms of classical evaluations constructed using the cohomology of the corresponding locally symmetric space and so-called automorphic cycles.