Few products, many h-fold sums

被引：3

作者：

Bush, Albert ^{[1
]}

Croot, Ernie ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, 686 Cherry St, Atlanta, GA 30332 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2018年 / 14卷 / 08期

关键词：

Sum-product problem; additive combinatorics; sumset and product set; Plunnecke-Ruzsa inequality; dependent random choice; SET; INTEGERS; NUMBER;

D O I：

10.1142/S1793042118501270

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Expanding upon a technique of Croot and Hart, we show that for every h, there exists an epsilon > 0 such that if A subset of R is sufficiently large and vertical bar A.A vertical bar <= vertical bar A vertical bar(1+epsilon), then vertical bar hA vertical bar >= vertical bar A vertical bar(Omega(e root log h)).

引用

页码：2107 / 2128

页数：22

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