Spacings between integers having typically many prime factors

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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 languageEnglish
Pages (from-to)102-117
Number of pages16
JournalCanadian Mathematical Bulletin
Volume53
Issue number1
DOIs
Publication statusPublished - Mar 2010
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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