Integral Moments of Automorphic L-functions

2006/12/15 by Adrian Diaconu, Diaconu, Adrian, Paul Garrett +1 · 1 citation
Mathematics · #11R42 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0612428

openalex publication_date 2006/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Zeros of Polynomials in Derivatives of Automorphic L-functions

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