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An approximation property of Pisot numbers (Articolo in rivista)
- Type
- Label
- An approximation property of Pisot numbers (Articolo in rivista) (literal)
- Anno
- 2000-01-01T00:00:00+01:00 (literal)
- Alternative label
Komornik, Vilmos; Loreti, Paola; Pedicini, Marco (2000)
An approximation property of Pisot numbers
in Journal of number theory (Print)
(literal)
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- Komornik, Vilmos; Loreti, Paola; Pedicini, Marco (literal)
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- ISI Web of Science (WOS) (literal)
- Titolo
- An approximation property of Pisot numbers (literal)
- Abstract
- Let $q>1$. Initiated by P. Erd\H os et al. in \cite{ErdJooKom1}, several authors
studied the numbers $l^m(q)=\inf \{y\ :\ y\in\Lambda_m,\ y\ne 0\}$,
$m=1,2,\dots$, where $\Lambda_m$ denotes the set of all finite sums of the form
$y=\eps_0 + \eps_1 q + \eps_2 q^2 + \dots + \eps_n q^n$
with integer coefficients $-m\le \eps_i \le m$. It is
known (\cite{Bug}, \cite{ErdJooKom1}, \cite{ErdKom}) that $q$ is a Pisot number
if and only if $l^m(q)>0$ for all $m$. The value of $l^1(q)$ was determined for
many particular Pisot numbers, but the general case remains widely open. In this
paper we determine the value of $l^m(q)$ in other cases. (literal)
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