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.

Reçu le : 2020-02-07
Révisé le : 2020-09-24
Accepté le : 2020-10-24
Publié le : 2021-01-08
DOI : https://doi.org/10.5802/jtnb.1145
Classification : 11R06,  11R80,  11J71
Mots clés : Salem numbers, Mahler measure, 2-Pisot numbers.
@article{JTNB_2020__32_3_877_0,
     author = {Toufik Za\"\i mi},
     title = {Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {877--889},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {32},
     number = {3},
     year = {2020},
     doi = {10.5802/jtnb.1145},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_877_0/}
}
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/item/JTNB_2020__32_3_877_0/

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