WHEN THE SIEVE WORKS

被引：12

作者：

Granville, Andrew ^{[1
]}

Koukoulopoulos, Dimitris ^{[1
]}

Matomaki, Kaisa ^{[2
]}

机构：

[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[2] Univ Turku, Dept Math & Stat, Turku, Finland

来源：

DUKE MATHEMATICAL JOURNAL | 2015年 / 164卷 / 10期

基金：

芬兰科学院; 加拿大自然科学与工程研究理事会;

关键词：

INTEGERS; NUMBER;

D O I：

10.1215/00127094-3120891

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are interested in classifying those sets of primes P such that when we sieve out the integers up to x by the primes in P-c we are left with roughly the expected number of unsieved integers. In particular, we obtain the first general results for sieving an interval of length x with primes including some in (root x, x], using methods motivated by additive combinatorics.

引用

页码：1935 / 1969

页数：35