Fourier-Jacobi expansion of automorphic forms on Sp (1, q) generating quaternionic discrete series

研究成果: Article

7 引用 (Scopus)

抄録

The aim of this paper is to develop the notion of the Fourier expansion of automorphic forms on Sp (1, q) generating quaternionic discrete series, which are non-holomorphic forms. There is such an expansion given by Tsuneo Arakawa, assuming the boundedness of the forms and the integrability of the discrete series. We study these automorphic forms without such assumptions. When q > 1 we prove the "Koecher principle" for such automorphic forms, whose validity is known for holomorphic automorphic forms except elliptic modular forms.

元の言語English
ページ(範囲)638-682
ページ数45
ジャーナルJournal of Functional Analysis
239
発行部数2
DOI
出版物ステータスPublished - 2006 10 15
外部発表Yes

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Automorphic Forms
Jacobi
Series
Fourier Expansion
Modular Forms
Integrability
Boundedness
Form

ASJC Scopus subject areas

  • Analysis

これを引用

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AB - The aim of this paper is to develop the notion of the Fourier expansion of automorphic forms on Sp (1, q) generating quaternionic discrete series, which are non-holomorphic forms. There is such an expansion given by Tsuneo Arakawa, assuming the boundedness of the forms and the integrability of the discrete series. We study these automorphic forms without such assumptions. When q > 1 we prove the "Koecher principle" for such automorphic forms, whose validity is known for holomorphic automorphic forms except elliptic modular forms.

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KW - Quaternionic discrete series

KW - The real symplectic group of signature (1 +, q -)

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