A converse theorem for Jacobi-Maass forms and applications

We provide a converse theorem for Jacobi-Maass forms, as introduced by Pitale (2009), and give three applications. Firstly, we generalize a converse theorem for holomorphic Jacobi cusp forms due to Martin (1996) to non-cuspidal Jacobi forms. Secondly, we prove the analogue result for skew-holomorphic Jacobi forms, and thirdly, we give a new proof for the existence of an explicit isomorphism between half integral weight Maass forms in Kohnen's plus space of level 4 and Jacobi-Maass forms of index 1, first proved by Pitale (2009).