  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.
