Visible lattice points along curves

被引：5

作者：

Liu, Kui ^{[1
]}

Meng, Xianchang ^{[2
]}

机构：

[1] Qingdao Univ, Sch Math & Stat, 308 Ningxia Rd, Qingdao, Shandong, Peoples R China

[2] Georg August Univ Gottingen, Math Inst, Bunsenstr 3-5, D-37073 Gottingen, Germany

来源：

RAMANUJAN JOURNAL | 2021年 / 56卷 / 03期

关键词：

Lattice points; Joint visibility; Mobius function; VISIBILITY;

D O I：

10.1007/s11139-020-00302-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some setSof 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.

引用

页码：1073 / 1086

页数：14

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