Integral Moments of Automorphic L-functions

Abstract

This paper exposes the underlying mechanism for obtaining second integral moments of $G{L}_2$ automorphic $L$--functions over an arbitrary number field. Here, moments for $G{L}_2$ 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 $\mathbb{Q}$, we recover the classical results.

41 pages