NEAR OPTIMAL BOUNDS IN FREIMAN'S THEOREM

被引：31

作者：

Schoen, Tomasz ^{[1
]}

机构：

[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland

来源：

DUKE MATHEMATICAL JOURNAL | 2011年 / 158卷 / 01期

关键词：

LONG ARITHMETIC PROGRESSIONS; SUMSETS; SETS; PROOF; ERDOS;

D O I：

10.1215/00127094-1276283

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if for a finite set A of integers we have vertical bar A + A vertical bar <= K vertical bar A vertical bar, then A is contained in a generalized arithmetic progression of dimension at most K1+C(log K)-1/2 and of size at most exp(K1+C(log K)-1/2)vertical bar A vertical bar for some absolute constant C. We also discuss a number of applications of this result.

引用

页码：1 / 12

页数：12

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