Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Density of Coprime m-tuples over Holomorphy Rings   Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of
genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of
places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we
compute the density of coprime $m$-tuples of elements of $H$. As a side result,
we obtain that whenever the complement of $\mathcal S$ is finite, the
computation of the density can be reduced to the computation of the
$L$-polynomial of the function field. In the rational function field case,
classical results for the density of coprime $m$-tuples of polynomials are
obtained as corollaries.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: alg-geom