### Abstract

We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for δ arbitrarily small and positive, the nearest neighbor spacings between integers n with |ω(n)-loglogn| < (loglogn)^{δ} obey the Poisson distribution law.

Original language | English |
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Pages (from-to) | 102-117 |

Number of pages | 16 |

Journal | Canadian Mathematical Bulletin |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Spacings between integers having typically many prime factors.** / Khan, Rizwanur.

Research output: Contribution to journal › Article

*Canadian Mathematical Bulletin*, vol. 53, no. 1, pp. 102-117. https://doi.org/10.4153/CMB-2010-022-8

}

TY - JOUR

T1 - Spacings between integers having typically many prime factors

AU - Khan, Rizwanur

PY - 2010/3

Y1 - 2010/3

N2 - We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for δ arbitrarily small and positive, the nearest neighbor spacings between integers n with |ω(n)-loglogn| < (loglogn)δ obey the Poisson distribution law.

AB - We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for δ arbitrarily small and positive, the nearest neighbor spacings between integers n with |ω(n)-loglogn| < (loglogn)δ obey the Poisson distribution law.

UR - http://www.scopus.com/inward/record.url?scp=77949369313&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949369313&partnerID=8YFLogxK

U2 - 10.4153/CMB-2010-022-8

DO - 10.4153/CMB-2010-022-8

M3 - Article

VL - 53

SP - 102

EP - 117

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 1

ER -