Publications de l'Institut Mathématique, Nouvelle Série Vol. 99(113), pp. 281–285 (2016) 

ON THE CONJUGATES OF CERTAIN ALGEBRAIC INTEGERSToufik ZaïmiDepartment of Mathematics and Statistics, College of Science, AlImam Mohammad Ibn Saud Islamic University, Riyadh, Kingdom of Saudi ArabiaAbstract: A wellknown theorem, due to C. J. Smyth, asserts that two conjugates of a Pisot number, having the same modulus are necessary complex conjugates. We show that this result remains true for $K$Pisot numbers, where $K$ is a real algebraic number field. Also, we prove that a $j$Pisot number, where $j$ is a natural number, can not have more than $2j$ conjugates with the same modulus. Keywords: Pisot numbers; Salem numbers; special algebraic numbers Classification (MSC2000): 11R06; 11R04; 12D10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.
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