Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers
Journal de théorie des nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 877-889.

Motivé par une question de M. J. Bertin, on obtient des paramétrisations des polynômes minimaux des nombres de Salem quartiques, disons α, qui sont des mesures de Mahler des 2 -nombres de Pisot non-réciproques. Cela nous permet de déterminer de tels nombres α, de trace donnée, et de déduire que pour tout entier naturel t (resp. t2), il y a un nombre de Salem quartique, de trace t, qui est (resp. qui n’est pas) une mesure de Mahler d’un 2 -nombre de Pisot non-réciproque.

Motivated by a question of M. J. Bertin, we obtain parametrizations of minimal polynomials of quartic Salem numbers, say α, which are Mahler measures of non-reciprocal 2-Pisot numbers. This allows us to determine all such numbers α with a given trace, and to deduce that for any natural number t (resp. t2) there is a quartic Salem number of trace t which is (resp. which is not) a Mahler measure of a non-reciprocal 2-Pisot number.

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DOI : 10.5802/jtnb.1145
Classification : 11R06, 11R80, 11J71
Mots clés : Salem numbers, Mahler measure, $2$-Pisot numbers.
Zaïmi, Toufik 1

1 Department of Mathematics and Statistics. College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU) P. O. Box 90950 Riyadh 11623 Saudi Arabia
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Zaïmi, Toufik. Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers. Journal de théorie des nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 877-889. doi : 10.5802/jtnb.1145. http://www.numdam.org/articles/10.5802/jtnb.1145/

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