The distribution of rationals in residue classes
| dc.creator | Cobeli, Cristian | |
| dc.creator | Zaharescu, Alexandru | |
| dc.date | 2005-11-14 | |
| dc.date.accessioned | 2026-07-07T08:07:22Z | |
| dc.date.available | 2026-07-07T08:07:22Z | |
| dc.description | Our purpose is to give an account of the $r$-tuple problem on the increasing sequence of reduced fractions having denominators bounded by a certain size and belonging to a fixed real interval. We show that when the size grows to infinity, the proportion of the $r$-tuples of consecutive denominators with components in certain apriori fixed arithmetic progressions with the same ratio approaches a limit, which is independent on the interval. The limit is given explicitly and it is completely described in a few particular instances. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511356 | |
| dc.identifier | http://arxiv.org/abs/math/0511356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130922 | |
| dc.subject | Number Theory | |
| dc.subject | Statistics Theory | |
| dc.subject | 11B57 (primary) | |
| dc.title | The distribution of rationals in residue classes | |
| dc.type | text |