On an approximation property of Pisot numbers II
Journal de Théorie des Nombres de Bordeaux, Volume 16 (2004) no. 1, pp. 239-249.

Let q be a complex number, m be a positive rational integer and l m (q)=inf{P(q),P m [X],P(q)0}, where m [X] denotes the set of polynomials with rational integer coefficients of absolute value m. We determine in this note the maximum of the quantities l m (q) when q runs through the interval ]m,m+1[. We also show that if q is a non-real number of modulus >1, then q is a complex Pisot number if and only if l m (q)>0 for all m.

Soit q un nombre complexe, m un entier positif et l m (q)=inf{P(q),P m [X],P(q)0}, où m [X] désigne l’ensemble des polynômes à coefficients entiers de valeur absolue m. Nous déterminons dans cette note le maximum des quantités l m (q) quand q décrit l’intervalle ]m,m+1[. Nous montrons aussi que si q est un nombre non-réel de module >1, alors q est un nombre de Pisot complexe si et seulement si l m (q)>0 pour tout m.

Published online:
DOI: 10.5802/jtnb.446
Toufik Zaïmi 1

1 King Saud University Dept. of Mathematics P. O. Box 2455 Riyadh 11451, Saudi Arabia
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Toufik Zaïmi. On an approximation property of Pisot numbers II. Journal de Théorie des Nombres de Bordeaux, Volume 16 (2004) no. 1, pp. 239-249. doi : 10.5802/jtnb.446. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.446/

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