Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The variance of arithmetic measures associated to closed geodesics on
  the modular surface   We determine the variance for the fluctuations of the arithmetic measures
obtained by collecting all closed geodesics on the modular surface with the
same discriminant and ordering them by the latter. This arithmetic variance
differs by subtle factors from the variance that one gets when considering
individual closed geodesics when ordered by their length. The arithmetic
variance is the same one that appears in the fluctuations of measures
associated with quantum states on the modular surface.

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The categories of this paper are: dg-ga
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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: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph