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.

中文翻译：

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沿曲线可见的晶格点

本文涉及平面中晶格点的数量，这些晶格点沿着某些曲线同时可见于某些点阵S中的所有元素。通过提出可见度级别的概念，我们能够在先前研究的定义中更仔细地分析“可见”点和“不可见”点。我们证明了在不同可见度水平下晶格点数量的渐近公式。