On a problem of K. Mahler: Diophantine approximation and Cantor sets
| dc.creator | Levesley, Jason | |
| dc.creator | Salp, Cem | |
| dc.creator | Velani, Sanju | |
| dc.date | 2005-05-04 | |
| dc.date.accessioned | 2026-07-07T05:19:38Z | |
| dc.date.available | 2026-07-07T05:19:38Z | |
| dc.description | Let $K$ denote the middle third Cantor set and ${\cal A}:= \{3^n : n = 0,1,2, >... \} $. Given a real, positive function $ψ$ let $ W_{\cal A}(ψ)$ denote the set of real numbers $x$ in the unit interval for which there exist infinitely many $(p,q) \in \Z \times {\cal A} $ such that $ |x - p/q| < ψ(q) $. The analogue of the Hausdorff measure version of the Duffin-Schaeffer conjecture is established for $ W_{\cal A}(ψ) \cap K $. One of the consequences of this is that there exist very well approximable numbers, other than Liouville numbers, in $K$ -- an assertion attributed to K. Mahler. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505074 | |
| dc.identifier | http://arxiv.org/abs/math/0505074 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75088 | |
| dc.subject | Number Theory | |
| dc.subject | Probability | |
| dc.subject | Primary 11J83; Secondary 11J82, 11K55 | |
| dc.title | On a problem of K. Mahler: Diophantine approximation and Cantor sets | |
| dc.type | text |