Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H-Harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Some
  Indefinite Theta Series   It was shown in previous work that the one-variable $\widehat\mu$-function
defined by Zwegers (and Zagier) and his indefinite theta series attached to
lattices of signature $(r\!+\!1,1)$ are both Heisenberg harmonic Maa\ss-Jacobi
forms. We extend the concept of Heisenberg harmonicity to Maa\ss-Jacobi forms
of arbitrary many elliptic variables, and produce indefinite theta series of
"product type" for non-degenerate lattices of signature $(r\!+\!s,s)$. We thus
obtain a clean generalization of $\widehat\mu$ to these negative definite
lattices. From restrictions to torsion points of Heisenberg harmonic
Maa\ss-Jacobi forms, we obtain harmonic weak Maa\ss\ forms of higher depth in
the sense of Zagier and Zwegers. In particular, we explain the modular
completion of some, so-called degenerate indefinite theta series in the context
of higher depth mixed mock modular forms. The structure theory for Heisenberg
harmonic Maa\ss-Jacobi forms developed in this paper also explains a curious
splitting of Zwegers's two-variable $\widehat\mu$-function into the sum of a
meromorphic Jacobi form and a one-variable Maa\ss-Jacobi form.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: physics