On the size of Kakeya sets in finite fields-Reference-Cited by-同舟云学术

On the size of Kakeya sets in finite fields

Published:2008-06-23 Issue:4 Volume:22 Page:1093-1097
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Dvir Zeev

Abstract

A Kakeya set is a subset of F n \mathbb {F}^n , where F \mathbb {F} is a finite field of q 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 ⋅ q n C_{n} \cdot q^{n} , where C n C_{n} depends only on n n . This answers a question of Wolff.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2009-22-04/S0894-0347-08-00607-3/S0894-0347-08-00607-3.pdf

Reference13 articles.

1. [AT08]AT08 N. Alon and T. Tao. Private communication. 2008.

2. A sum-product estimate in finite fields, and applications;Bourgain, J.;Geom. Funct. Anal.,2004

3. On the dimension of Kakeya sets and related maximal inequalities;Bourgain, J.;Geom. Funct. Anal.,1999

4. Harmonic analysis and combinatorics: how much may they contribute to each other?;Bourgain, J.,2000

5. Some remarks on the Kakeya problem;Davies, Roy O.;Proc. Cambridge Philos. Soc.,1971

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