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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Siegel modular forms of
half-integral weights and Jacobi forms


Author: Koichi Takase
Journal: Trans. Amer. Math. Soc. 351 (1999), 735-780
MSC (1991): Primary 11F37, 11F27; Secondary 11F70
MathSciNet review: 1466958
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Abstract: We will establish a bijective correspondence between the space of the cuspidal Jacobi forms and the space of the half-integral weight Siegel cusp forms which is compatible with the action of the Hecke operators. This correspondence is based on a bijective correspondence between the irreducible unitary representations of a two-fold covering group of a symplectic group and a Jacobi group (that is, a semidirect product of a symplectic group and a Heisenberg group). The classical results due to Eichler-Zagier and Ibukiyama will be reconsidered from our representation theoretic point of view.


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Additional Information

Koichi Takase
Affiliation: Department of Mathematics, Miyagi University of Education, Aoba-ku, Sendai 980, Japan
Email: f26508@cctu.cc.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02168-6
PII: S 0002-9947(99)02168-6
Received by editor(s): February 5, 1997
Article copyright: © Copyright 1999 American Mathematical Society