Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rogers' mean value theorem for $S$-arithmetic Siegel transform and
  applications to the geometry of numbers   We prove higher moment formulas for Siegel transforms defined over the space
of unimodular $S$-lattices in $\mathbb Q_S^d$, $d\ge 3$, where in the real
case, the formulas are introduced by Rogers (1955). As applications, we obtain
the random statements of Gauss circle problem for any convex sets in $\mathbb
Q_S^d$ containing the origin and of the effective Oppenheim conjecture for
$S$-arithmetic quadratic forms.

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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: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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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: hep-ph