English

On the Finite Field Kakeya Problem in Two Dimensions

Number Theory 2007-05-23 v2

Abstract

A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the size of such a subset and prove some results toward this conjecture.

Keywords

Cite

@article{arxiv.math/0510356,
  title  = {On the Finite Field Kakeya Problem in Two Dimensions},
  author = {X. W. C. Faber},
  journal= {arXiv preprint arXiv:math/0510356},
  year   = {2007}
}

Comments

9 pages; added mention of an alternate proof of the Incidence Formula; included mention of the recent related result of Joshua Cooper. to appear in "Journal of Number Theory"