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
相关论文
共 50 条
[31]   Loewner's "Forgotten" Theorem [J].
Albers, Peter ;
Tabachnikov, Serge .
MATHEMATICAL INTELLIGENCER, 2022, 44 (01) :7-11
[32]   SZEMEREDI'S THEOREM IN THE PRIMES [J].
Rimanic, Luka ;
Wolf, Julia .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2019, 62 (02) :443-457
[33]   Generalizing Parikh's Theorem [J].
Makowsky, Johann A. .
GAMES, NORMS AND REASONS: LOGIC AT THE CROSSROADS, 2011, 353 :163-+
[34]   ERDOS SEMI-GROUPS, ARITHMETIC PROGRESSIONS, AND SZEMEREDI'S THEOREM [J].
Yu, Han .
REAL ANALYSIS EXCHANGE, 2019, 44 (01) :101-118
[35]   Explicit bounds for rational points near planar curves and metric Diophantine approximation [J].
Beresnevich, Victor ;
Zorin, Evgeniy .
ADVANCES IN MATHEMATICS, 2010, 225 (06) :3064-3087
[36]   A density version of Cobham's theorem [J].
Byszewski, Jakub ;
Konieczny, Jakub .
ACTA ARITHMETICA, 2020, 192 (03) :235-247
[37]   Fujimoto's Theorem - a Further Study [J].
Banerjee, A. .
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2016, 51 (04) :199-207
[38]   MULTIVALUED VERSIONS OF A BOLZANO'S THEOREM [J].
Bae, Jong-Sook ;
Cho, Seong-Hoon .
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2011, 48 (03) :641-653
[39]   Porosity, Differentiability and Pansu's Theorem [J].
Pinamonti, Andrea ;
Speight, Gareth .
JOURNAL OF GEOMETRIC ANALYSIS, 2017, 27 (03) :2055-2080
[40]   SARKOZY'S THEOREM IN FUNCTION FIELDS [J].
Green, Ben .
QUARTERLY JOURNAL OF MATHEMATICS, 2017, 68 (01) :237-242
12345