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On the Fourier coefficients of positive index meromorphic Jacobi forms

Author: Sander Zwegers
Journal: Proc. Amer. Math. Soc. 143 (2015), 4211-4221
MSC (2010): Primary 11F30, 11F50
Published electronically: March 18, 2015
MathSciNet review: 3373921
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Abstract: Fourier coefficients of meromorphic Jacobi forms show up in the study of mock theta functions and Kac-Wakimoto characters. It has previously been shown that they are the holomorphic parts of certain vector-valued almost harmonic Maass forms. In this paper, we give an alternative characterization of these objects by applying the Maass lowering operator to the completions of the Fourier coefficients. We then obtain a formula in terms of classical theta functions and functions that behave like almost holomorphic modular forms.

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Sander Zwegers
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86–90, 50931 Cologne, Germany

Keywords: Jacobi forms, mock modular forms, almost holomorphic modular forms
Received by editor(s): March 28, 2014
Received by editor(s) in revised form: June 11, 2014
Published electronically: March 18, 2015
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2015 American Mathematical Society

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