Geodesic
On the Conjugates of Certain Algebraic Integers
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 281 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
DOI : 10.2298/PIM1613281Z
Classification : 11R06, 11R04, 12D10
Keywords: Pisot numbers, Salem numbers, special algebraic numbers 
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Toufik Zaïmi. On the Conjugates of Certain Algebraic Integers. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 281 . doi : 10.2298/PIM1613281Z. http://geodesic.mathdoc.fr/articles/10.2298/PIM1613281Z/

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