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

DOI:
https://doi.org/10.1090/S0894-0347-08-00607-3

Published electronically:
June 23, 2008

MathSciNet review:
2525780

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Abstract | References | Similar Articles | Additional Information

Abstract: A Kakeya set is a subset of , where is a finite field of elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least , where depends only on . 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:
https://doi.org/10.1090/S0894-0347-08-00607-3

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.