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On the Siegel–Weil formula: The case of singular forms

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  04 May 2011

Shunsuke Yamana
Shunsuke Yamana*
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan (email: yamana@sci.osaka-cu.ac.jp)
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Abstract

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For the dual pair Sp(n)×O(m) with m≤n, we prove an identity between a special value of a certain Eisenstein series and the regularized integral of a theta function. The proof uses the functional equation of the Eisenstein series and the regularized Siegel–Weil formula for Sp(n)×O(2n+2−m). Analogous results for unitary and orthogonal groups are included.

Keywords

Eisenstein seriesSiegel–Weil formulasingular forms

MSC classification

Secondary: 11F27: Theta series; Weil representation; theta correspondences 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011 , pp. 1003 - 1021
Copyright
Copyright © Foundation Compositio Mathematica 2011

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