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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On the size of Kakeya sets in finite fields


Author: Zeev Dvir
Journal: J. Amer. Math. Soc. 22 (2009), 1093-1097
MSC (2000): Primary 52C17; Secondary 05B25
Published electronically: June 23, 2008
MathSciNet review: 2525780
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Abstract: A Kakeya set is a subset of $ \mathbb{F}^n$, where $ \mathbb{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.


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Additional Information

Zeev Dvir
Affiliation: Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel
Email: zeev.dvir@weizmann.ac.il

DOI: http://dx.doi.org/10.1090/S0894-0347-08-00607-3
PII: S 0894-0347(08)00607-3
Keywords: Kakeya, finite fields, polynomial method
Received by editor(s): March 24, 2008
Published electronically: June 23, 2008
Additional Notes: Research was supported by a Binational Science Foundation (BSF) Grant.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.