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arXiv · 1810.12791

Logarithmic bounds for Roth's theorem via almost-periodicity

Thomas F. Bloom·Olof Sisask
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Abstract

We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \subset \{1,2,\ldots,N\}$ is free of three-term progressions, then $\lvert A\rvert \leq N/(\log N)^{1-o(1)}$. Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity.

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Thomas F. Bloom, Olof Sisask. 2019-05-09. Logarithmic bounds for Roth's theorem via almost-periodicity. https://doi.org/10.19086/da.7884

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