Distinct distances between points and lines in Fq2

被引：4

作者：

Thang Pham ^{[1
]}

Nguyen Duy Phuong ^{[2
]}

Nguyen Minh Sang ^{[2
]}

Valculescu, Claudiu ^{[1
]}

Le Anh Vinh ^{[3
]}

机构：

[1] EPF Lausanne, Dept Math, Lausanne, Switzerland

[2] Vietnam Natl Univ, Hanoi Univ Sci, Hanoi, Vietnam

[3] Vietnam Natl Univ, Univ Educ, Hanoi, Vietnam

来源：

FORUM MATHEMATICUM | 2018年 / 30卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Distinct distances; point-line incidences; finite fields; SUM-PRODUCT ESTIMATE; FINITE-FIELDS; SPACES;

D O I：

10.1515/forum-2016-0248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if we are given a set of points P and set of lines L in F-q(2) such that vertical bar P parallel to|L vertical bar >= q(8/3), then the set of distinct distances between points from P and lines from L contains a positive proportion of all distances. Using the same techniques, we also obtain a generalization of this result in higher dimensional cases.

引用

页码：799 / 808

页数：10

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