Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition

Bringmann, Kathrin; Raum, Martin; Richter, Olav

doi:10.1090/S0002-9947-2015-06418-6

Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition
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by Kathrin Bringmann, Martin Raum and Olav K. Richter PDF

Trans. Amer. Math. Soc. 367 (2015), 6647-6670 Request permission

Abstract:

Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms with singularities which includes the real-analytic Jacobi forms from Zwegers’s PhD thesis. We provide several structure results for the space of such Jacobi forms, and we employ Zwegers’s $\widehat {\mu }$-functions to establish a theta-like decomposition.

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