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An improvement to the Kelley-Meka bounds on three-term arithmetic progressions

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arxiv 2309.02353 v1 pith:G7NUHBTD submitted 2023-09-05 math.NT math.CO

Thomas F. Bloom , Olof Sisask This is my paper · ORCID
classification math.NTmath.CO
keywords arithmeticprogressionsthree-termnon-trivialboundboundsbreakthroughconclusion
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abstract

In a recent breakthrough Kelley and Meka proved a quasipolynomial upper bound for the density of sets of integers without non-trivial three-term arithmetic progressions. We present a simple modification to their method that strengthens their conclusion, in particular proving that if $A\subset\{1,\ldots,N\}$ has no non-trivial three-term arithmetic progressions then \[\lvert A\rvert \leq \exp(-c(\log N)^{1/9})N\] for some $c>0$.

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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  6. Large Sets of Integers with No Harmonic Triples

    math.NT 2026-07 accept novelty 6.0 of 10

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