A combinatorial characterization of Jacobi forms (Q1024944)

\textit{H. Cohen} [Lect. Notes Math. 627, 175--196 (1977; Zbl 0382.10020)] constructed a lift from elliptic modular forms to Hilbert modular forms over real quadratic fields. The proof was based on a combinatorial characterization of modular forms on \(\mathbb{H}^2\). In the paper under review the authors extend Cohen's characterization of modular forms to Jacobi forms on \(\mathbb{H}^2\times \mathbb{C}^2\).