WHEN THE SIEVE WORKS

被引：11

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：

加拿大自然科学与工程研究理事会; 芬兰科学院;

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

共 13 条

[1]

[Anonymous], PREPRINT

[2]

BLEICHENBACHER D., 1939, CONTINUOUS POS UNPUB

[3]

Friedlander J., 2010, OPERA CRIBRO

[4]

FRIEDLANDER JB, 1976, P LOND MATH SOC, V33, P565

[5] The number of unsieved integers up to x [J].

Granville, A ;

Soundararajan, K .

ACTA ARITHMETICA, 2004, 115 (04) :305-328

[6]

HALL RR, 1974, ACTA ARITH, V25, P347

[7] ON THE NUMBER OF POSITIVE INTEGERS GREATER-THAN-OR-EQUAL-TO X AND FREE OF PRIME FACTORS GREATER-THAN Y [J].

HILDEBRAND, A .

JOURNAL OF NUMBER THEORY, 1986, 22 (03) :289-307

[8] QUANTITATIVE MEAN-VALUE THEOREMS FOR NONNEGATIVE MULTIPLICATIVE FUNCTIONS-II [J].

HILDEBRAND, A .

ACTA ARITHMETICA, 1987, 48 (03) :209-260

[9]

IWANIEC H., 2004, AM MATH SOC C PUB, V53

[10]

LENSTRA JR H. W., 2005, PREPRINT

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