Integral Moments of Automorphic L-functions
Adrian Diaconu, Paul Garrett
Abstract
This paper exposes the underlying mechanism for obtaining second integral moments of GL2 automorphic L--functions over an arbitrary number field. Here, moments for GL2 are presented in a form enabling application of the structure of adele groups and their representation theory. To the best of our knowledge, this is the first formulation of integral moments in adele-group-theoretic terms, distinguishing global and local issues, and allowing uniform application to number fields. When specialized to the field of rational numbers Q, we recover the classical results.
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