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arXiv · 1207.5600

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

Kathrin Bringmann·Martin Raum·Olav Richter
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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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Kathrin Bringmann, Martin Raum, Olav Richter. 2012-07-24. Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition. https://arxiv.org/abs/1207.5600

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