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

共 50 条

[21] Inellipses of Convex Polygons, Brianchon's Theorem, and Bradley's Theorem
Tupan, Alexandru
AMERICAN MATHEMATICAL MONTHLY, 2021, 129 (01) : 4 - 23
[22] Computational Concentration of Measure: Optimal Bounds, Reductions, and More
Etesami, Omid
Mahloujifar, Saeed
Mahmoody, Mohammad
PROCEEDINGS OF THE 2020 ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SODA, 2020, : 345 - 363
[23] Computational Concentration of Measure: Optimal Bounds, Reductions, and More
Etesami, Omid
Mahloujifar, Saeed
Mahmoody, Mohammad
PROCEEDINGS OF THE THIRTY-FIRST ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA'20), 2020, : 345 - 363
[24] A maximal extension of the best-known bounds for the Furstenberg-Sarkozy theorem
Rice, Alex
ACTA ARITHMETICA, 2019, 187 (01) : 1 - 41
[25] ON THE NEAR-EQUALITY CASE OF THE POSITIVE MASS THEOREM
Lee, Dan A.
DUKE MATHEMATICAL JOURNAL, 2009, 148 (01) : 63 - 80
[26] A GENERAL NONLINEAR VERSION OF ROTH'S THEOREM ON THE REAL LINE
Li, Xiang
Yan, Dunyan
Yu, Haixia
Zhang, Xingsong
JOURNAL OF MATHEMATICAL INEQUALITIES, 2021, 15 (03): : 1119 - 1153
[27] A GUIDE TO CARLESON'S THEOREM
Demeter, Ciprian
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2015, 45 (01) : 169 - 212
[28] EUCLID'S THEOREM REDUX
Delo, Ben
Saidak, Filip
FIBONACCI QUARTERLY, 2019, 57 (04): : 331 - 336
[29] SZEMEREDI'S THEOREM IN THE PRIMES
Rimanic, Luka
Wolf, Julia
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2019, 62 (02) : 443 - 457
[30] Loewner's "Forgotten" Theorem
Albers, Peter
Tabachnikov, Serge
MATHEMATICAL INTELLIGENCER, 2022, 44 (01) : 7 - 11

← 1 2 3 4 5 →