Some new results about Jacobi forms (Q1369762)

In the paper under review the author deals with Jacobi forms on \(\mathbb{H}_n \times M(n \times j; \mathbb{C})\), where \(\mathbb{H}_n\) is the Siegel half-space of degree \(n\). He considers Jacobi forms of weight \(k\) and index \(s\) in the sense of \textit{C. Ziegler} [Abh. Math. Semin. Univ. Hamb. 59, 191-224 (1989; Zbl 0707.11035)], where \(2s\) is even and unimodular. In this case the space of Jacobi forms is isomorphic to the space of Siegel modular forms of degree \(n\) and weight \(k-j/2\). This situation allows for a description of singular and strongly singular Jacobi forms as well as estimates for the Fourier coefficients of cusp forms.