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Spacings Between Integers Having Typically Many Prime Factors

  Published:2009-12-04
 Printed: Mar 2010
  • Rizwanur Khan
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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 $\delta$ arbitrarily small and positive, the nearest neighbor spacings between integers n with $|\omega(n) - log log n| < (log log n)^{\delta}$ obey the Poisson distribution law.
MSC Classifications: 11K99 show english descriptions None of the above, but in this section 11K99 - None of the above, but in this section
 

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