Adelization of Automorphic Distributions and Mirabolic Eisenstein Series

Details Adelization of Automorphic Distributions and Mirabolic Eisenstein Series Adelization of Automorphic Distributions and Mirabolic Eisenstein Series

2011-06-14

arxiv.org/abs/1106.2583v1

Mathematics

Number Theory

46 pages, to appear in Contemporary Mathematics, volume in honor of Gregg Zuckerman's 60th birthday edited by Jeff Adams, Bong

Scientific paper

Automorphic representations can be studied in terms of the embeddings of abstract models of representations into spaces of functions on Lie groups that are invariant under discrete subgroups. In this paper we describe an adelic framework to describe them for the group GL(n,R), and provide a detailed analysis of the automorphic distributions associated to the mirabolic Eisenstein series. We give an explicit functional equation for some distributional pairings involving this mirabolic Eisenstein distribution, and the action of intertwining operators.

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