Eisenstein series and the cubic moment for PGL(2)

Eisenstein series and the cubic moment for PGL(2)

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Paul Nelson, ETH Zürich
IAS - Simonyi Hall Seminar Room SH-101

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.