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Logarithmic bounds for Roth's theorem via almost-periodicity
Univ Cambridge, Dept Pure Math & Math Stat, Cambridge, England.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2019 (English)In: DISCRETE ANALYSIS, ISSN 2397-3129, article id 4Article in journal (Refereed) Published
Abstract [en]

We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if A subset of {1, 2,..., N} is free of three- term progressions, then vertical bar A vertical bar <= N/(logN)(1-o(1)). Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity.

Place, publisher, year, edition, pages
2019. article id 4
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Computer Sciences
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URN: urn:nbn:se:uu:diva-384065DOI: 10.19086/da.7884ISI: 000467651400001OAI: oai:DiVA.org:uu-384065DiVA, id: diva2:1327898
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Swedish Research Council, 2013-4896Available from: 2019-06-20 Created: 2019-06-20 Last updated: 2019-06-20Bibliographically approved

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