On large subsets of Fnq with no three-termarithmetic progression

Jordan S. Ellenberg, Dion Gijswijt

Research output: Contribution to journalArticleScientificpeer-review

41 Downloads (Pure)

Abstract

In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a subset of F n q  Fqn with no three terms in arithmetic progression by c n  cn with c<q c<q . For q=3 q=3 , the problem of finding the largest subset of F n 3  F3n with no three terms in arithmetic progression is called the cap set problem. Previously the best known upper bound for the affine cap problem, due to Bateman and Katz, was on order n −1−ϵ 3 n  n−1−ϵ3n .
Original languageEnglish
Pages (from-to)339-343
Number of pages5
JournalAnnals of Mathematics
Volume185
Issue number1
DOIs
Publication statusPublished - 2017

Bibliographical note

Accepted author manuscript

Keywords

  • additive combinatorics
  • additive number theory
  • arithmetic progressions
  • cap sets

Fingerprint

Dive into the research topics of 'On large subsets of F<i>nq</i> with no three-termarithmetic progression'. Together they form a unique fingerprint.

Cite this