On alpha-adic expansions in Pisot bases
| dc.creator | Ambroz, P. | |
| dc.creator | Frougny, C. | |
| dc.date | 2006-03-28 | |
| dc.date.accessioned | 2026-07-07T07:07:17Z | |
| dc.date.available | 2026-07-07T07:07:17Z | |
| dc.description | We study $α$-adic expansions of numbers in an extension field, that is to say, left infinite representations of numbers in the positional numeration system with the base $α$, where $α$ is an algebraic conjugate of a Pisot number $β$. Based on a result of Bertrand and Schmidt, we prove that a number belongs to $\mathbb{Q}(α)$ if and only if it has an eventually periodic $α$-expansion. Then we consider $α$-adic expansions of elements of the extension ring $\mathbb{Z}[α^{-1}]$ when $β$ satisfies the so-called Finiteness property (F). In the particular case that $β$ is a quadratic Pisot unit, we inspect the unicity and/or multiplicity of $α$-adic expansions of elements of $\mathbb{Z}[α^{-1}]$. We also provide algorithms to generate $α$-adic expansions of rational numbers. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603650 | |
| dc.identifier | http://arxiv.org/abs/math/0603650 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110334 | |
| dc.subject | Number Theory | |
| dc.subject | 11A63; 11R06 | |
| dc.title | On alpha-adic expansions in Pisot bases | |
| dc.type | text |