A converse theorem for Jacobi–Maass forms and applications

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Abstract

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).

Original languageEnglish
Pages (from-to)41-61
Number of pages21
JournalJournal of Number Theory
Volume169
DOIs
StatePublished - 1 Dec 2016

Keywords

  • Converse theorem
  • Dirichlet series
  • Functional equation
  • Jacobi–Maass forms

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