On the size of kakeya sets in finite fields

Journal of the American Mathematical Society

Volumn 22, Issue 4, 2009, Pages 1093-1097

  Dvir, Zeev ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Finite fields; Kakeya; Polynomial method

Indexed keywords

EID: 70349831495     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-08-00607-3     Document Type: Article

References (13)

1. N. Alon and T. Tao. Private communication. 2008.
2. J. Bourgain, N. Katz, and T. Tao. A sum-product estimate in finite fields, and applications. GAFA, 14(1):27-57, 2004. MR2053599 (2005d:11028) (Pubitemid 38640645)
3. J. Bourgain. On the dimension of Kakeya sets and related maximal inequalities. Geom. Funct. Anal., (9) : 256-282, 1999. MR1692486 (2000b:42013)
4. J. Bourgain. Harmonic analysis and combinatorics: How much may they contribute to each other? IMU/Amer. Math. Soc., pages 13-32, 2000. MR1754764 (2001c:42009)
5. R. Davies. Some remarks on the Kakeya problem. Proc. Cambridge Philos. Soc., (69) : 417-421, 1971. MR0272988 (42:7869)
6. N. Katz and T. Tao. Bounds on arithmetic projections, and applications to the Kakeya conjecture. Math. Res. Letters, 6: 625-630, 1999. MR1739220 (2000m:28006)
7. G. Mockenhaupt and T. Tao. Restriction and Kakeya phenomena for finite fields. Duke Math. J., 121: 35-74, 2004. MR2031165 (2004m:11200) (Pubitemid 38411249)
8. K. M Rogers. The finite field Kakeya problem. Amer. Math. Monthly, 108(8):756-759, 2001. MR1865664 (2002g:11175) (Pubitemid 33585532)
9. J. T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. J. ACM, 27(4):701-717, 1980. MR594695 (82m:68078)
10. T. Tao. From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE. Notices Amer. Math. Soc., 48(3):294-303, 2001. MR1820041 (2002b:42021)
11. T. Tao. A new bound for finite field Besicovitch sets in four dimensions. Pacific J. Math., 222(2):337-363, 2005. MR2225076 (2007c:11027) (Pubitemid 43221450)
12. T. Wolff. Recent work connected with the Kakeya problem. Prospects in mathematics (Princeton, NJ, 1996), pages 129-162, 1999. MR1660476 (2000d:42010)
13. R. Zippel. Probabilistic algorithms for sparse polynomials. In Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, pages 216-226, Springer- Verlag, 1979. MR575692 (81g:68061)