A note on Jacobi forms of higher degree (Q1912806)

The authors consider the space of holomorphic Jacobi forms of degree \(n\), weight \(k\) and integer-valued index \(\mu\) for the group \(\text{Sp} (n, \mathbb{Z}) \ltimes H_\mathbb{Z}^{(n, 1)}\). They show that this space is at most one-dimensional for certain values of \(k\) and \(2\leq n\leq 5\). The proof uses a modification of \textit{M. Eichler}'s idea [Math. Ann. 213, 281-291 (1975; Zbl 0289.10020)] in the case of Siegel modular forms.