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Logarithmic bounds for Roth's theorem via almost-periodicity (1810.12791v2)
Published 30 Oct 2018 in math.CO and math.NT
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.