Logarithmic bounds for Roth's theorem via almost-periodicity

DOI10.19086/da.7884zbMath1472.11055arXiv1810.12791OpenAlexW2898996103MaRDI QIDQ5211003

Thomas F. Bloom, Olof Sisask

Publication date: 17 January 2020

Published in: discrete Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12791

zbMATH Keywords

new proof of logarithmic boundsRoth's theorem on arithmetic progressions

Mathematics Subject Classification ID

Arithmetic progressions (11B25) Harmonic analysis and almost periodicity in probabilistic number theory (11K70) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (8)

The equidistant dimension of graphs ⋮ The number of \(k\)-dimensional corner-free subsets of grids ⋮ Tower-type bounds for Roth's theorem with popular differences ⋮ A NOTE ON POWERFUL NUMBERS IN SHORT INTERVALS ⋮ Roth's theorem and the Hardy-Littlewood majorant problem for thin subsets of primes ⋮ The Kelley-Meka bounds for sets free of three-term arithmetic progressions ⋮ A subexponential upper bound for van der Waerden numbers \(W(3,k)\) ⋮ Improved bound in Roth's theorem on arithmetic progressions

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• New bounds on cap sets
• A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1.
• Additive structures in sumsets
• Integer Sets Containing No Arithmetic Progressions
• Arithmetic Progressions in Sumsets and L^p-Almost-Periodicity
• On Certain Sets of Integers

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