New bounds on cap sets

Authors:
Michael Bateman and Nets Hawk Katz

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

Published electronically:
November 29, 2011

MathSciNet review:
2869028

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Abstract | References | Similar Articles | Additional Information

Abstract: We provide an improvement over Meshulam's bound on cap sets in . We show that there exist universal and so that any cap set in has size at most . We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.

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Additional 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

Email:
nhkatz@indiana.edu

DOI:
https://doi.org/10.1090/S0894-0347-2011-00725-X

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

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.