EXACT FORMULAS FOR COEFFICIENTS OF JACOBI FORMS

In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincare series, as well as Zwegers' real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this paper, we give exact formulas for the Fourier coefficients of the holomorphic parts of harmonic Maass-Jacobi forms and, in particular, we obtain explicit formulas for the Fourier coefficients of weak Jacobi forms.