Distinct distances between points and lines in 𝔽q2

Authors: Phạm Văn Thắng, Nguyễn Duy Phương, Nguyễn Minh Sáng, Claudiu Valculescu, Lê Anh Vinh,

https://doi.org/10.1515/forum-2016-0248.

Publisher, magazine: ,

Publication year: 2018

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Abstract

We prove that if we are given a set of points P and set of lines L in 픽 2 q such that |P||L| ≳ 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.

Tags: Distinct distances, point-line incidences, finite fields