Finite field Kakeya and Nikodym sets in three dimensions

Ben Lund, Shubhangi Saraf, Charles Wolf

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We give improved lower bounds on the size of Kakeya and Nikodym sets over F 3 q . We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines in F 3 q and show that this conjecture implies an optimal bound on the size of a Nikodym set.

Original languageEnglish
Pages (from-to)2836-2849
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Volume32
Issue number4
DOIs
StatePublished - 1 Jan 2018
Externally publishedYes

Keywords

  • Finite fields
  • Geometric incidences
  • Kakeya problem

ASJC Scopus subject areas

  • Mathematics (all)

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