Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers
Toufik Zaïmi1
1 Department of Mathematics and Statistics. College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU) P. O. Box 90950 Riyadh 11623 Saudi Arabia
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. t≥2), 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. t≥2) 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.
Toufik Zaïmi 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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Toufik Zaïmi. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1145/

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