On a Generalization of Szemeredi's Theorem
Number Theory
2007-05-23 v1 Dynamical Systems
Abstract
Let A \subseteq [1,..,N]^2 be a set of cardinality at least N^2/(log log N)^c, where c>0 is an absolute constant. We prove that A contains a triple {(k,m), (k+d,m), (k,m+d)}, where d>0. This theorem is a two-dimensional generalization of Szemeredi's theorem on arithmetic progression.
Cite
@article{arxiv.math/0503639,
title = {On a Generalization of Szemeredi's Theorem},
author = {I. D. Shkredov},
journal= {arXiv preprint arXiv:math/0503639},
year = {2007}
}
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51 pages