We generalize Weil's converse theorem to Jacobi cusp forms of weight k, index m and Dirichlet character χ over the group Γ 0 (N ) Z 2 . Then two applications of this result are given; we generalize a construction of Jacobi forms due to Skogman and present a new proof for several known lifts of such Jacobi forms to half-integral weight modular forms.
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