Spacings between integers having typically many prime factors

Rizwanur Khan

doi:10.4153/CMB-2010-022-8

Spacings between integers having typically many prime factors

Rizwanur Khan

Research output: Contribution to journal › Article

1 Citation (Scopus)

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
Pages (from-to)	102-117
Number of pages	16
Journal	Canadian Mathematical Bulletin
Volume	53
Issue number	1
DOIs	https://doi.org/10.4153/CMB-2010-022-8
Publication status	Published - Mar 2010
Externally published	Yes

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ASJC Scopus subject areas

Mathematics(all)

Cite this

Khan, R. (2010). Spacings between integers having typically many prime factors. Canadian Mathematical Bulletin, 53(1), 102-117. https://doi.org/10.4153/CMB-2010-022-8

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Access to Document

10.4153/CMB-2010-022-8