Joint IAS/Princeton University Number Theory Seminar

Eisenstein series and the cubic moment for PGL(2)

We will discuss how to study the cubic moment of any family of automorphic L-functions on PGL(2) using regularized diagonal periods of Eisenstein series, following a strategy suggested by Michel--Venkatesh. Applications include generalizations to the setting of number fields of some results of Conrey--Iwaniec and Petrow--Young, improved estimates for representation numbers of ternary quadratic forms over number fields, and improvements to the prime geodesic theorem on arithmetic hyperbolic 3-folds.

Date & Time

January 30, 2020 | 4:30pm – 5:30pm

Location

Simonyi Hall 101

Speakers

Paul Nelson, Aarhus University

Affiliation

ETH Zürich

Event Series

Categories