New bounds on cap sets
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- by Michael Bateman and Nets Hawk Katz
- J. Amer. Math. Soc. 25 (2012), 585-613
- DOI: https://doi.org/10.1090/S0894-0347-2011-00725-X
- Published electronically: November 29, 2011
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Abstract:
We provide an improvement over Meshulam’s bound on cap sets in $F_3^N$. We show that there exist universal $\epsilon >0$ and $C>0$ so that any cap set in $F_3^N$ has size at most $C {3^N \over N^{1+\epsilon }}$. We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.References
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Bibliographic Information
- Michael Bateman
- Affiliation: Department of Mathematics, UCLA, Los Angeles, California 90095
- Email: bateman@math.ucla.edu
- Nets Hawk Katz
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405-7000
- MR Author ID: 610432
- Email: nhkatz@indiana.edu
- Received by editor(s): April 2, 2011
- Received by editor(s) in revised form: October 28, 2011
- Published electronically: November 29, 2011
- Additional Notes: The first author is supported by an NSF postdoctoral fellowship, DMS-0902490
The second author is partially supported by NSF grant DMS-1001607 - © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 25 (2012), 585-613
- MSC (2010): Primary 11T71; Secondary 05D40
- DOI: https://doi.org/10.1090/S0894-0347-2011-00725-X
- MathSciNet review: 2869028