Arithmetic progressions in sumsets

被引：49

作者：

Green, B ^{[1
]}

机构：

[1] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ, England

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2002年 / 12卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Structural Result; Arithmetic Progression; Positive Real;

D O I：

10.1007/s00039-002-8258-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove several results concerning arithmetic progressions in sets of integers. Suppose, for example, that alpha and beta are positive reals, that N is a large prime and that C, D subset of or equal to Z/NZ have sizes gammaN and deltaN respectively. Then the sumset C + D contains an AP of length at least e(crootlog N), where c > 0 depends only on gamma and delta. In deriving these results we introduce the concept of hereditary non-uniformity (HNU) for subsets of Z/NZ, and prove a structural result for sets with this property.

引用

页码：584 / 597

页数：14

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