Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of
  Compact Hyperbolic 3-manifolds   In this paper, we numerically investigate the length spectra and the
low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large
number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero
eigenvalues have been successfully computed using the periodic orbit sum
method, which are compared with various geometric quantities such as volume,
diameter and length of the shortest periodic geodesic of the manifolds. The
deviation of low-lying eigenvalue spectra of manifolds converging to a cusped
hyperbolic manifold from the asymptotic distribution has been measured by
$\zeta-$ function and spectral distance.

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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph