Fourier expansion of holomorphic modular forms on classical lie groups of tube type along the minimal parabolic subgroup

H. Narita

doi:10.1007/BF02941540

Fourier expansion of holomorphic modular forms on classical lie groups of tube type along the minimal parabolic subgroup

H. Narita^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

For holomorphic modular forms on tube domains, there are two types of known Fourier expansions, i.e. the classical Fourier expansion and the Fourier-Jacobi expansion. Either of them is along a maximal parabolic subgroup. In this paper, we discuss Fourier expansion of holomorphic modular forms on tube domains of classical type along the minimal parabolic subgroup. We also relate our Fourier expansion to the two known ones in terms of Fourier coefficients and theta series appearing in these expansions.

Original language	English
Pages (from-to)	253-279
Number of pages	27
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	74
Issue number	1
DOIs	https://doi.org/10.1007/BF02941540
Publication status	Published - 2004 Dec 1
Externally published	Yes

Keywords

Fourier expansion
Generalized Whittaker function
Tube domains

ASJC Scopus subject areas

Mathematics(all)

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10.1007/BF02941540

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abstract = "For holomorphic modular forms on tube domains, there are two types of known Fourier expansions, i.e. the classical Fourier expansion and the Fourier-Jacobi expansion. Either of them is along a maximal parabolic subgroup. In this paper, we discuss Fourier expansion of holomorphic modular forms on tube domains of classical type along the minimal parabolic subgroup. We also relate our Fourier expansion to the two known ones in terms of Fourier coefficients and theta series appearing in these expansions.",

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AB - For holomorphic modular forms on tube domains, there are two types of known Fourier expansions, i.e. the classical Fourier expansion and the Fourier-Jacobi expansion. Either of them is along a maximal parabolic subgroup. In this paper, we discuss Fourier expansion of holomorphic modular forms on tube domains of classical type along the minimal parabolic subgroup. We also relate our Fourier expansion to the two known ones in terms of Fourier coefficients and theta series appearing in these expansions.

KW - Fourier expansion

KW - Generalized Whittaker function

KW - Tube domains

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Fourier expansion of holomorphic modular forms on classical lie groups of tube type along the minimal parabolic subgroup

Abstract

Keywords

ASJC Scopus subject areas

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