Corpus ID: 220381133

Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions

@inproceedings{Bloom2020BreakingTL,
  title={Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions},
  author={Thomas F. Bloom and Olof Sisask},
  year={2020}
}
  • Thomas F. Bloom, Olof Sisask
  • Published 2020
  • Mathematics
  • We show that if A ⊂ {1, . . . , N} contains no non-trivial three-term arithmetic progressions then |A| ≪ N/(logN) for some absolute constant c > 0. In particular, this proves the first non-trivial case of a conjecture of Erdős on arithmetic progressions. 

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 26 REFERENCES
    Improved bound in Roth's theorem on arithmetic progressions
    2
    Roth’s theorem on progressions revisited
    99
    On certain other sets of integers
    35
    On Roth's theorem on progressions
    134
    Roth's theorem in the primes
    138
    Progression-free sets in Z_4^n are exponentially small
    73
    A quantitative improvement for Roth's theorem on arithmetic progressions
    78
    Improving Roth's Theorem in the Primes
    18
    On Subsets of Finite Abelian Groups with No 3-Term Arithmetic Progressions
    137
    A Note on Elkin’s Improvement of Behrend’s Construction
    54