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 language | English |
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Pages (from-to) | 10-18 |
Number of pages | 9 |
Journal | Mathematische Nachrichten |
Volume | 288 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2015 Jan 1 |
Externally published | Yes |
Keywords
- 11F50
- 11F67
- Eichler cohomology
- Jacobi form
ASJC Scopus subject areas
- Mathematics(all)