The theory of Jacobi forms over the Cayley numbers

Eie, M.; Krieg, A.

doi:10.1090/S0002-9947-1994-1195510-8

The theory of Jacobi forms over the Cayley numbers
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by M. Eie and A. Krieg PDF

Trans. Amer. Math. Soc. 342 (1994), 793-805 Request permission

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.

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