On the size of Kakeya sets in finite fields
Abstract
A Kakeya set is a subset of {F}^n , where {F} is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least C_{n} \cdot q^{n} , where C_{n} depends only on n . This answers a question of Wolff.
 Publication:

Journal of the American Mathematical Society
 Pub Date:
 October 2009
 DOI:
 10.1090/S0894034708006073
 arXiv:
 arXiv:0803.2336
 Bibcode:
 2009JAMS...22.1093D
 Keywords:

 Kakeya;
 finite fields;
 polynomial method;
 Mathematics  Combinatorics;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Number Theory;
 52C17
 EPrint:
 Improved bound and added references