# 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} }

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.

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