On the Density of Coprime m-tuples over Holomorphy Rings
On the Density of Coprime m-tuples over Holomorphy Rings
复制标题
关于全纯环上互质m元组的密度
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Schnyder
中科院分区：
文献类型：
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作者：
Giacomo Micheli;R. Schnyder
设$\mathbb F_q$是一个有限域，$F/\mathbb F_q$是亏格为g$的函数域，其上有一个满常域$\mathbb F_q$，$\mathcal S$是$F$的一个位置集，$H$是$\mathcal S$的一个全纯环。本文计算了H的元素互素m-元组的密度。作为一个副结果，我们得到，只要$\mathcal S$的补是有限的，密度的计算可以减少到计算的$L$-多项式的功能领域。在有理函数域的情况下，作为推论，得到了多项式互素$m$-元组的稠密性的经典结果。
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.