Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed Divisor of a Multivariate Polynomial and Generalized Factorials in
  Several Variables   We define new generalized factorials in several variables over an arbitrary
subset $\underline{S} \subseteq R^n,$ where $R$ is a Dedekind domain and $n$ is
a positive integer. We then study the properties of the fixed divisor
$d(\underline{S},f)$ of a multivariate polynomial $f \in R[x_1,x_2, \ldots,
x_n]$. We generalize the results of Polya, Bhargava, Gunji & McQuillan and
strengthen that of Evrard, all of which relate the fixed divisor to generalized
factorials of $\underline{S}$. We also express $d(\underline{S},f)$ in terms of
the images $f(\underline{a})$ of finitely many elements $\underline{a} \in
R^n$, generalizing a result of Hensel, and in terms of the coefficients of $f$
under explicit bases.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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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: plasm-ph