On the Farey fractions with denominators in arithmetic progression
| dc.creator | Cobeli, Cristian | |
| dc.creator | Zaharescu, Alexandru | |
| dc.date | 2005-11-14 | |
| dc.date.accessioned | 2026-07-07T06:51:14Z | |
| dc.date.available | 2026-07-07T06:51:14Z | |
| dc.description | Let $F_Q$ be the set of Farey fractions of order $Q$. Given the integers $\d\ge 2$ and $0\le \c \le \d-1$, let $F_Q(c,d)$ be the subset of $F_Q$ of those fractions whose denominators are $\equiv c \pmod d$, arranged in ascending order. The problem we address here is to show that as $Q\to\infty$, there exists a limit probability measuring the distribution of $s$-tuples of consecutive denominators of fractions in $F_Q(c,d)$. This shows that the clusters of points $(q_0/Q,q_1/Q,...,q_s/Q)\in[0,1]^{s+1}$, where $q_0,q_1,...,q_s$ are consecutive denominators of members of $F_Q$ produce a limit set, denoted by $D(c,d)$. The shape and the structure of this set are presented in several particular cases. | |
| dc.description | 28 pages, 52 figures | |
| dc.identifier | https://arxiv.org/abs/math/0511358 | |
| dc.identifier | http://arxiv.org/abs/math/0511358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104919 | |
| dc.subject | Number Theory | |
| dc.subject | 11B57 (primary) | |
| dc.title | On the Farey fractions with denominators in arithmetic progression | |
| dc.type | text |