On the Intervals of a Third between Farey Fractions
| 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 | The spacing distribution between Farey points has drawn attention in recent years. It was found that the gaps $γ_{j+1}-γ_j$ between consecutive elements of the Farey sequence produce, as $Q\to\infty$, a limiting measure. Numerical computations suggest that for any $d\ge 2$, the gaps $γ_{j+d}-γ_j$ also produce a limiting measure whose support is distinguished by remarkable topological features. Here we prove the existence of the spacing distribution for $d=2$ and characterize completely the corresponding support of the measure. | |
| dc.description | 12 pages, one figure | |
| dc.identifier | https://arxiv.org/abs/math/0511363 | |
| dc.identifier | http://arxiv.org/abs/math/0511363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104921 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37 (primary), 11BB57 (secondary) | |
| dc.title | On the Intervals of a Third between Farey Fractions | |
| dc.type | text |