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Toufik Zaimi
Commentaires sur quelques résultats sur les nombres de Pisot
Journal de théorie des nombres de Bordeaux, 22 no. 2 (2010), p. 513-524, doi: 10.5802/jtnb.729
Article PDF | Reviews MR 2769076 | Zbl 1223.11130

Résumé - Abstract

Using some results of Yves Meyer on harmonious sets, we prove that a real number $\theta >1$ is a Pisot number if and only if $A_{[\theta ]}\cup (-A_{[\theta ]}),$ where $A_{[\theta ]}$ is the set of polynomials with coefficients in $\lbrace 0,1,...,[\theta ]\rbrace$ evaluated at $\theta ,$ is a Meyer set. This allows us to deduce certain related results of Y. Bugeaud or P. Erdös and V. Komornik. By the same tools we also show that for $\varepsilon \in ]0,1],$ the set of $\varepsilon$-Pisot numbers which are contained in a real algebraic number field $K$ and have the same degree as $K,$ is a Meyer set.
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