Abstract
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)⋉ℤ2. 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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Y. Martin was partially supported by Fondecyt grant 1090094.
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Martin, Y., Osses, D. On the analogue of Weil’s converse theorem for Jacobi forms and their lift to half-integral weight modular forms. Ramanujan J 26, 155–183 (2011). https://doi.org/10.1007/s11139-010-9258-x
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DOI: https://doi.org/10.1007/s11139-010-9258-x