# Geodesic restrictions of Maass forms and moments of Hecke $L$-functions

Speaker: Peter Humphries

Date: Thu, Jul 28, 2022

Conference: Moments of L-functions Workshop

Subject:

Class: Scientific

### Abstract:

How large are the $L^2$-restrictions of automorphic forms to closed geodesics? I will discuss how this problem can be shown to be equivalent to proving bounds for certain weighted moments of Hecke $L$-functions, and how the lattice structure of the ring of integers of real quadratic numbers fields can be exploited to obtain essentially optimal upper bounds for these weighted moments.