On the analogue of Weil's converse theorem for Jacobi forms and their lift to half-integral weight modular forms (Q411280)

In an earlier paper \textit{Y. Martin} [J. Number Theory 61, 181--193 (1996; Zbl 0869.11044)] derived a converse theorem for Jacobi forms in the sense of Eichler/Zagier. In the paper under review the authors derive an analogous result for Jacobi cusp forms of weight \(k\), index \(m\) and Dirichlet character \(\chi\) over \(\Gamma_0(N)\ltimes \mathbb{Z}^2\). Applications concern a result of Skogman as well as liftings of Jacobi forms to modular forms of half-integral weight.