Pairings of automorphic distributions

Stephen D. Miller; Wilfried Schmid

doi:10.1007/s00208-011-0685-9

Pairings of automorphic distributions

Stephen D. Miller, Wilfried Schmid

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	581-597
Number of pages	17
Journal	Mathematische Annalen
Volume	353
Issue number	2
DOIs	https://doi.org/10.1007/s00208-011-0685-9
State	Published - Jun 2012

All Science Journal Classification (ASJC) codes

Mathematics(all)

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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.",

author = "Miller, {Stephen D.} and Wilfried Schmid",

note = "Funding Information: Partially supported by NSF Grants DMS-0500922 and DMS-0601009, and DARPA Grant HR0011-04-1-0031.",

year = "2012",

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AU - Schmid, Wilfried

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AB - 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.

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Pairings of automorphic distributions

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