On sets of integers not containing long arithmetic progressions

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We construct subsets of {1,...,N} of cardinality at least N exp(-C(log N)^{1/(k+1)}) which do not contain arithmetic progressions of length 2^k+1. This extends a result of Behrend (1946) concerning sets which do not contain aritmetic progressions of length 3.
8 pages

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Combinatorics, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/62064

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108155
 http://arxiv.org/abs/math/0108155

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arXiv