On a two-dimensional analogue of Szemeredi's theorem in Abelian groups

被引：3

作者：

Shkredov, I. D. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia

来源：

IZVESTIYA MATHEMATICS | 2009年 / 73卷 / 05期

关键词：

two-dimensional generalizations of Szemeredi's theorem; problems on arithmetic progressions; Roth's theorem; Bohr sets; ARITHMETIC PROGRESSIONS; ROTHS THEOREM; REGULARITY; SUBSETS; GOWERS; PROOF;

D O I：

10.1070/IM2009v073n05ABEH002472

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite Abelian group and A subset of G x G a set of cardinality at least vertical bar G vertical bar(2)/(log log vertical bar G vertical bar)(c), where c > 0 is air absolute constant. We prove that A contains a triple {(k,m), (k + d, m), (k,m + d)} with d not equal 0. This is a two-dimensional generalization of Szemeredi's theorem on arithmetic progressions.

引用

页码：1033 / 1075

页数：43

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