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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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New bounds on cap sets
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by Michael Bateman and Nets Hawk Katz
J. Amer. Math. Soc. 25 (2012), 585-613
Published electronically: November 29, 2011


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.
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Bibliographic Information
  • Michael Bateman
  • Affiliation: Department of Mathematics, UCLA, Los Angeles, California 90095
  • Email:
  • Nets Hawk Katz
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405-7000
  • MR Author ID: 610432
  • Email:
  • 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:
  • MathSciNet review: 2869028