论文标题
在数值平行的互补的互补上，最大的常见分隔线
Greatest Common Divisors on the Complement of Numerically Parallel Divisors
论文作者
论文摘要
我们证明了涉及数值平行分隔的积分点最大函数的不平等，从而推广了Wang和Yasufuku的结果（在Bugeaud-Corvaja-Zannier，Corvaja-Zannier工作之后，Corvaja-Zannier和第二作者）。在对Semiabelian品种的亚变量的积分点上应用了VOJTA的结果后，我们使用几何和高度理论将$ \ Mathbb {g} _m^n $的（已知）情况降低。除了在更广泛的环境中证明结果外，我们还研究了此设置中的特殊设置，包括计数函数和接近性函数。
We prove inequalities involving greatest common divisors of functions at integral points with respect to numerically parallel divisors, generalizing a result of Wang and Yasufuku (after work of Bugeaud-Corvaja-Zannier, Corvaja-Zannier, and the second author). After applying a result of Vojta on integral points on subvarieties of semiabelian varieties, we use geometry and the theory of heights to reduce to the (known) case of $\mathbb{G}_m^n$. In addition to proving results in a broader context than previously considered, we also study the exceptional set in this setting, for both the counting function and the proximity function.
