Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tauberian Approach to an Analog of Weyl's law for the Kohn Laplacian
  on Compact Heisenberg Manifolds   Let $M= \Gamma \setminus \mathbb{H}_d$ be a compact quotient of the
$d$-dimensional Heisenberg group $\mathbb{H}_d$ by a lattice subgroup $\Gamma$.
We show that the eigenvalue counting function $N(\lambda)$ for any fixed
element of a family of second order differential operators
$\left\{\mathcal{L}_\alpha\right\}$ on $M$ has asymptotic behavior
$N\left(\lambda\right) \sim C_{d,\alpha} \operatorname{vol}\left(M\right)
\lambda^{d + 1}$, where $C_{d,\alpha}$ is a constant that only depends on the
dimension $d$ and the parameter $\alpha$. As a consequence, we obtain an analog
of Weyl's law (both on functions and forms) for the Kohn Laplacian on $M$. Our
main tools are Folland's description of the spectrum of $\mathcal{L}_{\alpha}$
and Karamata's Tauberian theorem.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol