Note on the prime divisors of Farey fractions
Let P1(n) ≥ P2(n) ≥· · · be the prime divisors of a natural number n arranged in the non-increasing order. The limit distribution of the sequences (log Pi(mn)/ log(mn), i ≥ 1) for m/n ꞓ 2 (lambda1; lambda2), n ≤ x, are considered. It is proved that under some conditions on lambdai the limit distribu...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2011-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/14853 |
| _version_ | 1811321619192217600 |
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| author | Vytautas Kazakevičius Vilius Stakėnas |
| author_facet | Vytautas Kazakevičius Vilius Stakėnas |
| author_sort | Vytautas Kazakevičius |
| collection | DOAJ |
| description | Let P1(n) ≥ P2(n) ≥· · · be the prime divisors of a natural number n arranged in the non-increasing order. The limit distribution of the sequences (log Pi(mn)/ log(mn), i ≥ 1) for m/n ꞓ 2 (lambda1; lambda2), n ≤ x, are considered. It is proved that under some conditions on lambdai the limit distribution of the sequences exists and is closely related to the Poisson–Dirichlet distribution. |
| first_indexed | 2024-04-13T13:20:53Z |
| format | Article |
| id | doaj.art-9b891566a3324ba388365a470a3bf37d |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-04-13T13:20:53Z |
| publishDate | 2011-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-9b891566a3324ba388365a470a3bf37d2022-12-22T02:45:19ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2011-12-0152proc. LMS10.15388/LMR.2011.al03Note on the prime divisors of Farey fractionsVytautas Kazakevičius0Vilius Stakėnas1Vilnius UniversityVilnius UniversityLet P1(n) ≥ P2(n) ≥· · · be the prime divisors of a natural number n arranged in the non-increasing order. The limit distribution of the sequences (log Pi(mn)/ log(mn), i ≥ 1) for m/n ꞓ 2 (lambda1; lambda2), n ≤ x, are considered. It is proved that under some conditions on lambdai the limit distribution of the sequences exists and is closely related to the Poisson–Dirichlet distribution.https://www.journals.vu.lt/LMR/article/view/14853rational numbersprime divisorsPoisson-Dirichlet distribution |
| spellingShingle | Vytautas Kazakevičius Vilius Stakėnas Note on the prime divisors of Farey fractions Lietuvos Matematikos Rinkinys rational numbers prime divisors Poisson-Dirichlet distribution |
| title | Note on the prime divisors of Farey fractions |
| title_full | Note on the prime divisors of Farey fractions |
| title_fullStr | Note on the prime divisors of Farey fractions |
| title_full_unstemmed | Note on the prime divisors of Farey fractions |
| title_short | Note on the prime divisors of Farey fractions |
| title_sort | note on the prime divisors of farey fractions |
| topic | rational numbers prime divisors Poisson-Dirichlet distribution |
| url | https://www.journals.vu.lt/LMR/article/view/14853 |
| work_keys_str_mv | AT vytautaskazakevicius noteontheprimedivisorsoffareyfractions AT viliusstakenas noteontheprimedivisorsoffareyfractions |