A converse theorem for Jacobi-Maass forms and applications

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• 作者：Sebastiá ; n Herrero-Miranda ^{sdherrero@mat.puc.cl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11F37 ; 11F50 ; 11F66
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：169
• 期：Complete
• 页码：41-61
• 全文大小：387 K

文摘

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).