## 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.## References

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## Additional Information

**Kathrin Bringmann**- Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany
- MR Author ID: 774752
- Email: kbringma@math.uni-koeln.de
**Martin Raum**- Affiliation: Department of Mathematics, ETH Zurich, Rämistrasse 101, CH-8092 Zürich, Switzerland
- Address at time of publication: Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany
- Email: martin@raum-brothers.eu
**Olav K. Richter**- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- ORCID: 0000-0003-3886-0893
- Email: richter@unt.edu
- Received by editor(s): June 21, 2013
- Received by editor(s) in revised form: February 18, 2014
- Published electronically: January 15, 2015
- Additional Notes: The first author was partially supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation and by NSF grant DMS-$0757907$. The second author held a scholarship from the Max Planck Society and is supported by the ETH Zurich Postdoctoral Fellowship Program and by the Marie Curie Actions for People COFUND Program. The third author was partially supported by Simons Foundation grant $\#200765$
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**367**(2015), 6647-6670 - MSC (2010): Primary 11F50; Secondary 11F60, 11F55, 11F37, 11F30, 11F27
- DOI: https://doi.org/10.1090/S0002-9947-2015-06418-6
- MathSciNet review: 3356950