Archimedean zeta integrals on U(2,1)

It is known that for a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain automorphic L-functions, which have applications to arithmetic. In this paper we explicitly calculate archimedean zeta integrals of this typ...

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Bibliographic Details
Published in:Journal of functional analysis 2015-07, Vol.269 (1), p.229-270
Main Author: Liu, Dongwen
Format: Article
Language:English
Subjects:
Discrete series
Matrix coefficients
Theta correspondence
Zeta integrals
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Summary:It is known that for a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain automorphic L-functions, which have applications to arithmetic. In this paper we explicitly calculate archimedean zeta integrals of this type for U(2,1). In particular we compute the matrix coefficients of Weil representations using joint harmonics in the Fock model, and those of discrete series using Schmid operators.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2015.04.003