The distribution of integers with at least two divisors in a short interval
| dc.creator | Ford, Kevin | |
| dc.creator | Tenenbaum, Gerald | |
| dc.date | 2006-07-19 | |
| dc.date | 2007-02-09 | |
| dc.date.accessioned | 2026-07-07T08:44:06Z | |
| dc.date.available | 2026-07-07T08:44:06Z | |
| dc.description | Let H(x,y,z) be the number of integers $\le x$ with a divisor in (y,z] and let H_1(x,y,z) be the number of integers $\le x$ with exactly one such divisor. When y and z are close, it is expected that H_1(x,y,z) H(x,y,z), that is, an integer with a divisor in (y,z] usually has just one. We determine necessary and sufficient conditions on y and z so that H_1(x,y,z) H(x,y,z). In doing so, we answer an open question from the paper "The distribution of integers with a divisor in a given interval", math.NT/0401223. | |
| dc.description | 12 pages; minor corrections; added abstract and affiliation information | |
| dc.identifier | https://arxiv.org/abs/math/0607460 | |
| dc.identifier | http://arxiv.org/abs/math/0607460 | |
| dc.identifier | Quart. J. Math. Oxford 58 (2007), 187-201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142539 | |
| dc.subject | Number Theory | |
| dc.subject | 11N25 | |
| dc.title | The distribution of integers with at least two divisors in a short interval | |
| dc.type | text |