### Abstract

We prove that, for a given Jacobi integral F, there is a harmonic Maass-Jacobi form such that its holomorphic part is F, and that the converse is also true. As an application, we construct a pairing between two Jacobi integrals that is defined by special values of partial L-functions of skew-holomorphic Jacobi cusp forms. We obtain connections between this pairing and the Petersson inner product for skew-holomorphic Jacobi cusp forms. This result can be considered as an analogue of the Haberland formula of elliptic modular forms for Jacobi forms.

Original language | English |
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Pages (from-to) | 442-467 |

Number of pages | 26 |

Journal | Journal of Number Theory |

Volume | 157 |

DOIs | |

Publication status | Published - 2015 Dec 1 |

Externally published | Yes |

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### Keywords

- Haberland formula
- Harmonic Maass-Jacobi form
- Jacobi integral
- Primary
- Secondary

### ASJC Scopus subject areas

- Algebra and Number Theory