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On the size of Kakeya sets in finite fields

Author(s): Zeev Dvir
Journal: J. Amer. Math. Soc.
MSC (2000): Primary 52C17; Secondary 05B25
Posted: June 23, 2008
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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: 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
Posted: June 23, 2008
Additional Notes: Research was supported by a Binational Science Foundation (BSF) Grant.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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