沿曲线的可见晶格点

摘要：

本文讨论了平面上沿某些曲线对某个格点集S中的所有元素同时可见的格点的个数。可见度概念的提出，使我们能够更细致地分析以往研究定义中的“可见”点和“不可见”点。我们证明了在不同的可见度水平的晶格点的数量的渐近公式。

英文摘要：

This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze more carefully about both the "visible" points and the "invisible" points in the definition of previous research. We prove asymptotic formulas for the number of lattice points in different levels of visibility.

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