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Spacings Between Integers Having Typically Many Prime Factors |
Canad. Math. Bull. 53(2010), 102-117
Published:2009-12-04
Printed: Mar 2010
Printed: Mar 2010
- Rizwanur Khan
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 - None of the above, but in this section |