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Three-term arithmetic progressions and sumsets

Part of: Sequences and sets Additive number theory; partitions

Published online by Cambridge University Press:  02 February 2009

Tom Sanders
Tom Sanders
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK (t.sanders@dpmms.cam.ac.uk)
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Abstract

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Suppose that G is an abelian group and that A ⊂ G is finite and contains no non-trivial three-term arithmetic progressions. We show that |A+A| »ε|A|(log|A|)⅓−ε.

Keywords

sumsetarithmetic progressionsFourier transform

MSC classification

Secondary: 11P55: Applications of the Hardy-Littlewood method 11B25: Arithmetic progressions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 211 - 233
Copyright
Copyright © Edinburgh Mathematical Society 2009