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

Hiro aki Narita

doi:10.1016/j.jfa.2006.03.015

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

Hiro aki Narita^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	638-682
Number of pages	45
Journal	Journal of Functional Analysis
Volume	239
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2006.03.015
Publication status	Published - 2006 Oct 15
Externally published	Yes

Keywords

Fourier expansion
Generalized Whittaker functions
Koecher principle
Quaternionic discrete series
The real symplectic group of signature (1 +, q -)

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2006.03.015

Cite this

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

abstract = "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.",

keywords = "Fourier expansion, Generalized Whittaker functions, Koecher principle, Quaternionic discrete series, The real symplectic group of signature (1 +, q -)",

author = "Narita, {Hiro aki}",

note = "Funding Information: 1 The author was partly supported by the Grant-in-Aid for JSPS Fellows, The Ministry of Education, Culture, Sports, Science and Technology, Japan for April 2002 to March 2005. The results of this paper were obtained in this period.",

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AU - Narita, Hiro aki

N1 - Funding Information: 1 The author was partly supported by the Grant-in-Aid for JSPS Fellows, The Ministry of Education, Culture, Sports, Science and Technology, Japan for April 2002 to March 2005. The results of this paper were obtained in this period.

PY - 2006/10/15

Y1 - 2006/10/15

N2 - 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.

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.

KW - Fourier expansion

KW - Generalized Whittaker functions

KW - Koecher principle

KW - Quaternionic discrete series

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

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DO - 10.1016/j.jfa.2006.03.015

M3 - Article

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SP - 638

EP - 682

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

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

Abstract

Keywords

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