Number of prime factors with a given multiplicity
| dc.contributor.author | Elma, Ertan | |
| dc.contributor.author | Liu, Yu-Ru | |
| dc.date.accessioned | 2023-10-03T15:15:31Z | |
| dc.date.available | 2023-10-03T15:15:31Z | |
| dc.date.issued | 2022-03 | |
| dc.description | This article has been published in a revised form in the Canadian Mathematical Bulletin https://doi.org/10.4153/S0008439521000266. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Canadian Mathematical Society 2021 | en |
| dc.description.abstract | Let k ⩾ 1 be a natural number and ωk (n) denote the number of distinct prime factors of a natural number n with multiplicity k. We estimate the first and second moments of the functions ωk with k ⩾ 1. Moreover, we prove that the function ω1(n) has normal order log log n and the function (ω1(n) − log log n)/√log log n has a normal distribution. Finally, we prove that the functions ωk (n) with k ⩾ 2 do not have normal order F(n) for any nondecreasing nonnegative function F. | en |
| dc.identifier.uri | https://doi.org/10.4153/s0008439521000266 | |
| dc.identifier.uri | http://hdl.handle.net/10012/20007 | |
| dc.language.iso | en | en |
| dc.publisher | Cambridge University Press | en |
| dc.relation.ispartofseries | Canadian Mathematical Bulletin;65(1) | |
| dc.subject | prime divisors | en |
| dc.subject | normal order | en |
| dc.subject | normal distribution | en |
| dc.title | Number of prime factors with a given multiplicity | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Elma, E., & Liu, Y.-R. (2021). Number of prime factors with a given multiplicity. Canadian Mathematical Bulletin, 65(1), 253–269. https://doi.org/10.4153/s0008439521000266 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |