Prime divisors are poisson distributed

被引：15

作者：

Granville, Andrew ^{[1
]}

机构：

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

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2007年 / 3卷 / 01期

关键词：

prime divisors; local distribution; permutation; poisson; Hardy-Ramanujan; factorization;

D O I：

10.1142/S1793042107000778

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the set of prime factors of almost all integers are "Poisson distributed", and that this remains true ( appropriately formulated) even when we restrict the number of prime factors of the integer. Our results have inspired analogous results about the distribution of cycle lengths of permutations.

引用

页码：1 / 18

页数：18

共 5 条

[1] Arratia R., 1997, NOT AM MATH SOC, V44, P903
[2] THE INTERMEDIATE PRIME DIVISORS OF INTEGERS
DEKONINCK, JM
GALAMBOS, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 101 (02) : 213 - 216
[3] Galambos J., 1976, Acta Arith., V31, P213
[4] ON THE NUMBER OF PRIME FACTORS OF AN INTEGER
HILDEBRAND, A
TENENBAUM, G
[J]. DUKE MATHEMATICAL JOURNAL, 1988, 56 (03) : 471 - 501
[5] A rate estimate in Billingsley's theorem for the size distribution of large prime factors
Tenenbaum, G
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 2000, 51 : 385 - 403

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