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 | |
| 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.
In: Canadian Mathematical Bulletin, Vol. 53, No. 1, 03.2010, p. 102-117.Research output: Contribution to journal › Article
}
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.
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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 -