Integral Moments of Automorphic L-functions

Details Integral Moments of Automorphic L-functions Integral Moments of Automorphic L-functions

2006-12-15

arxiv.org/abs/math/0612428v1

Mathematics

Number Theory

41 pages

Scientific paper

This paper exposes the underlying mechanism for obtaining second integral moments of $GL_2$ automorphic $L$--functions over an arbitrary number field. Here, moments for $GL_2$ 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 $\Bbb{Q}$, we recover the classical results.

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