Geodesic restrictions of Maass forms and moments of Hecke $L$-functions
Speaker: Peter Humphries
Date: Thu, Jul 28, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Thu, Jul 28, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
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.
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