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.
Bibliographical noteFunding Information:
The authors were supported by Samsung Science and Technology Foundation under Project SSTF-BA1301-11 .
© 2015 Elsevier Inc.
- Haberland formula
- Harmonic Maass-Jacobi form
- Jacobi integral
ASJC Scopus subject areas
- Algebra and Number Theory