Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of non-holomorphic modular forms III: real analytic cusp forms
  for $\mathrm{SL}_2(\mathbb{Z})$   We define canonical real analytic versions of modular forms of integral
weight for the full modular group, generalising real analytic Eisenstein
series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier
coefficients involve periods and quasi-periods of cusp forms, which are
conjecturally transcendental. In particular, we settle the question of finding
explicit `weak harmonic lifts' for every eigenform of integral weight $k$ and
level one. We show that mock modular forms of integral weight are
algebro-geometric and have Fourier coefficients proportional to $n^{1-k}(a'_n +
\rho a_n)$ for $n\neq 0$, where $\rho$ is the normalised permanent of the
period matrix of the corresponding motive, and $a_n, a'_n$ are the Fourier
coefficients of a Hecke eigenform and a weakly holomorphic Hecke eigenform,
respectively. More generally, this framework provides a conceptual explanation
for the algebraicity of the coefficients of mock modular forms in the CM case.

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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th