On the rational approximations to the powers of an algebraic number
| dc.creator | Corvaja, Pietro | |
| dc.creator | Zannier, Umberto | |
| dc.date | 2004-03-30 | |
| dc.date.accessioned | 2026-07-07T05:06:54Z | |
| dc.date.available | 2026-07-07T05:06:54Z | |
| dc.description | About fifty years ago Mahler proved that if $α>1$ is rational but not an integer and if $0<l<1$ then the fractional part of $α^n$ is $>l^n$ apart from a finite set of integers $n$ depending on $α$ and $l$. Answering completely a question of Mahler we show that the same conclusion holds for all algebraic numbers which are not $d$-th roots of Pisot numbers. By related methods, we also answer a question by Mendes France, characterizing completely the quadratic irrationals $α$ such that the continued fraction of $α^n$ has period length tending to infinity. | |
| dc.description | 12 pages, plain Tex | |
| dc.identifier | https://arxiv.org/abs/math/0403522 | |
| dc.identifier | http://arxiv.org/abs/math/0403522 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70649 | |
| dc.subject | Number Theory | |
| dc.subject | 11j25 | |
| dc.title | On the rational approximations to the powers of an algebraic number | |
| dc.type | text |