ON A THEOREM OF PLUNNECKE CONCERNING THE SUM OF A BASIS AND A SET OF POSITIVE DENSITY

被引：3

作者：

MALOUF, JL ^{[1
]}

机构：

[1] UNIV ILLINOIS,DEPT MATH,URBANA,IL 61801

来源：

JOURNAL OF NUMBER THEORY | 1995年 / 54卷 / 01期

关键词：

D O I：

10.1006/jnth.1995.1098

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1935 Erdos proved that every additive basis I of order h is an essential component by showing sigma(A + B) greater than or equal to sigma(A) + (1/2h) sigma(A)(1 - sigma(A)), where sigma denotes Schnirelmann density. This lower bound was improved by Pliinnecke to sigma(A + B) greater than or equal to sigma(A)(1-1/h), giving the best exponent. A simplified proof is presented. (C) 1995 Academic Press, Inc.

引用

页码：12 / 22

页数：11