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Fourier coefficients of Jacobi forms over Cayley numbers. (English) Zbl 0824.11032

In an earlier paper the author and the reviewer [The theory of Jacobi forms over the Cayley numbers, Trans. Am. Math. Soc. 342, 793-805 (1994)] explicitly studied Jacobi forms on \({\mathcal H} \times \mathbb{C}^ 8\), where \({\mathcal H}\) is the complex upper half-plane and \(\mathbb{C}^ 8\) is realized in terms of the Cayley numbers over \(\mathbb{C}\). In the paper under review the author investigates the attached Eisenstein series of weight \(k\) and index \(m\). The Fourier coefficients are calculated explicitly. They turn out to be finite products of certian geometric sums.
Reviewer: A.Krieg (Aachen)

MSC:

11F50 Jacobi forms
11F30 Fourier coefficients of automorphic forms
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