Pairings of automorphic distributions
Number Theory
2011-06-14 v1 Representation Theory
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.
Cite
@article{arxiv.1106.2364,
title = {Pairings of automorphic distributions},
author = {Stephen D. Miller and Wilfried Schmid},
journal= {arXiv preprint arXiv:1106.2364},
year = {2011}
}
Comments
19 pages, to appear in Mathematische Annalen