Pairings of automorphic distributions

2011/06/13 by Stephen D. Miller, Miller, Stephen D., Wilfried Schmid +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1106.2364

19 pages, to appear in Mathematische Annalen

arxiv created 2011/06/13 · openalex publication_date 2011/06/13 · arxiv updated 2011/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a pairing of automorphic distributions that applies in situations where a Lie group acts with an open orbit on a product of generalized flag varieties. The pairing gives meaning to an integral of products of automorphic distributions on these varieties. This generalizes classical integral representations or "Rankin-Selberg integrals" of L-functions, and gives new constructions and analytic continuations of automorphic L-functions. Keywords: Automorphic forms, invariant pairings, automorphic distributions, L-functions, analytic continuation, rapid decay.

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