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/S0894-0347-08-00607-3
- 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
- E-Print:
- Improved bound and added references