On distinct perpendicular bisectors and pinned distances in finite fields

Brandon Hanson, Ben Lund, Oliver Roche-Newton

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Given a set of points P ⊂ Fq2 such that |P| ≥ q4/3, we establish that for a positive proportion of points a ∈ P, we have|{∥a-b∥:b∈P}|蠑q, where ∥a-b∥ is the distance between points a and b. This improves a result of Chapman et al. [6]. A key ingredient of our proof also shows that, if |P| ≥ q3/2, then the number B of distinct lines which arise as the perpendicular bisector of two points in P satisfies B 蠑 q2.

Original languageEnglish (US)
Pages (from-to)240-264
Number of pages25
JournalFinite Fields and their Applications
Volume37
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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