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

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ON THE CONJUGATES OF CERTAIN ALGEBRAIC INTEGERS

Toufik Zaïmi

Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh, Kingdom of Saudi Arabia

Abstract: A well-known 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

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Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.

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