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
收藏
页码：1 / 12
页数：12
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