On dimension formulas for Jacobi forms. (English) Zbl 1257.11048
The authors consider Jacobi forms of integral weight \(k\) and index \(S\) being a positive definite half-integral \(l\times l\) matrix, which are defined on \(\mathcal{H}_n\times \mathbb{C}^{\; l\times n}\), where \(\mathcal{H}_n\) is the Siegel half-space of degree \(n\). These kinds of Jacobi forms were systematically treated by C. Ziegler [Abh. Math. Semin. Univ. Hamb. 59, 191–224 (1989; Zbl 0707.11035)]. In this paper the Selberg trace formula is described explicitly. An application yields an explicit formula of the dimension of the space of Jacobi cusp forms in the case \(n=2, k>l+4, l\) even.
Reviewer: Aloys Krieg (Aachen)
MSC:
| 11F50 | Jacobi forms |
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 11F72 | Spectral theory; trace formulas (e.g., that of Selberg) |
Citations:
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