New bounds on cap sets
Authors:
Michael Bateman and Nets Hawk Katz
Journal:
J. Amer. Math. Soc. 25 (2012), 585613
MSC (2010):
Primary 11T71; Secondary 05D40
Published electronically:
November 29, 2011
MathSciNet review:
2869028
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Abstract 
References 
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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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 T. Sanders, A note on Freiman's theorem in vector spaces, Combin. Probab. Comput. 17 (2008), 297305. MR 2396355 (2009a:11024)
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 T. Sanders, Structure in Sets with Logarithmic Doubling, Arxiv 1002.1552.
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 T. Sanders, On Roth's Theorem on Progressions, Arxiv 1011.0104.
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 I. Shkredov, On sets of large trigonometric sums, 2008 Izv. Ross. Akad. Nauk Ser. Math. 72, pp. 161182. MR 2394976 (2009e:11151)
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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 474057000
Email:
nhkatz@indiana.edu
DOI:
http://dx.doi.org/10.1090/S08940347201100725X
PII:
S 08940347(2011)00725X
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, DMS0902490
The second author is partially supported by NSF grant DMS1001607
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
