Comments on some results about Pisot numbers (Q628846)

A Meyer set is a relatively dense subset \(\Lambda\) of \({{\mathbb R}}^m \) such that \(\Lambda-\Lambda\) is uniformly discrete. The author proves that a real number \(\theta >1\) is a Pisot number if and only if \(A_{ [\theta ] }\cup (-A_{ [\theta ] })\) is a Meyer set, where \(A_{ [\theta ] }\) is the set of polynomials with coefficients in \(\{ 0,1,\ldots,[\theta ]\} \) evaluated at \(\theta\). 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.