Polynomial configurations in difference sets

被引：13

作者：

Lyall, Neil ^{[1
]}

Magyar, Akos ^{[1
]}

机构：

[1] Univ Georgia, Dept Math, Boyd Grad Studies Res Ctr, Athens, GA 30602 USA

来源：

JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 02期

关键词：

Difference sets; Sarkozy's theorem; Polynomial configurations; NO ARITHMETIC PROGRESSIONS; INTEGER SETS; THEOREM;

D O I：

10.1016/j.jnt.2008.05.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a quantitative result on the existence of linearly independent polynomial configurations in the difference set of sparse subsets of the integers. This result is achieved by first establishing a higher dimensional analogue of a theorem of Sarkozy and then applying a simple lifting argument. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：439 / 450

页数：12

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