On the Fourier coefficients of positive index meromorphic Jacobi forms

Zwegers, Sander

doi:10.1090/S0002-9939-2015-12581-6

On the Fourier coefficients of positive index meromorphic Jacobi forms
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Proc. Amer. Math. Soc. 143 (2015), 4211-4221 Request permission

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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