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Transactions of the American Mathematical Society

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The theory of Jacobi forms over the Cayley numbers


Authors: M. Eie and A. Krieg
Journal: Trans. Amer. Math. Soc. 342 (1994), 793-805
MSC: Primary 11F55; Secondary 11F27, 11F72
DOI: https://doi.org/10.1090/S0002-9947-1994-1195510-8
MathSciNet review: 1195510
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Abstract: As a generalization of the classical theory of Jacobi forms we discuss Jacobi forms on $ \mathcal{H} \times {\mathbb{C}^8}$, which are related with integral Cayley numbers. Using the Selberg trace formula we give a simple explicit formula for the dimension of the space of Jacobi forms. The orthogonal complement of the space of cusp forms is shown to be spanned by certain types of Eisenstein series.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1195510-8
Keywords: Jacobi form, Eisenstein series, theta series, vector valued elliptic modular form, Selberg trace formula
Article copyright: © Copyright 1994 American Mathematical Society

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