A quantitative improvement for Roth's theorem on arithmetic progressions

Thomas F Bloom

Research output: Contribution to journalArticle (Academic Journal)peer-review

38 Citations (Scopus)
267 Downloads (Pure)


We improve the quantitative estimate for Roth's theorem on three-term arithmetic progressions, showing that if A⊂{1,…,N} contains no non-trivial three-term arithmetic progressions, then ∣A∣≪N(loglogN)4/logN. By the same method, we also improve the bounds in the analogous problem over Fq[t] and for the problem of finding long arithmetic progressions in a sumset.
Original languageEnglish
Pages (from-to)643-663
Number of pages21
JournalJournal of the London Mathematical Society
Issue number3
Early online date25 Apr 2016
Publication statusPublished - 1 Jun 2016


  • 11B25 (primary)
  • 11B30
  • 11T55 (secondary)

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