We will discuss how to study the cubic moment of any family of automorphic L-functions on PGL2 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.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
