Cohomological relation between Jacobi forms and skew-holomorphic Jacobi forms

Dohoon Choi, Subong Lim

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Eichler and Zagier developed a theory of Jacobi forms to understand and extend Maass' work on the Saito-Kurokawa conjecture. Later Skoruppa introduced skew-holomorphic Jacobi forms, which play an important role in understanding liftings of modular forms and Jacobi forms. In this paper, we explain a relation between Jacobi forms and skew-holomorphic Jacobi forms in terms of a group cohomology. More precisely, we introduce an isomorphism from the direct sum of the space of Jacobi cusp forms on ΓJ and the space of skew-holomorphic Jacobi cusp forms on ΓJ with the same half-integral weight to the Eichler cohomology group of ΓJ with a coefficient module coming from polynomials.

Original languageEnglish
Pages (from-to)10-18
Number of pages9
JournalMathematische Nachrichten
Volume288
Issue number1
DOIs
Publication statusPublished - 2015 Jan 1
Externally publishedYes

Keywords

  • 11F50
  • 11F67
  • Eichler cohomology
  • Jacobi form

ASJC Scopus subject areas

  • Mathematics(all)

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