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Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers
Journal article   Open access  Peer reviewed

Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers

Toufik Zaimi
Journal de theorie des nombres de bordeaux, Vol.32(3), pp.877-889
01/01/2020

Abstract

Mathematics Physical Sciences Science & Technology
Motivated by a question of M. J. Bertin, we obtain parametrizations of minimal polynomials of quartic Salem numbers, say alpha, which are Mahler measures of non-reciprocal 2-Pisot numbers. This allows us to determine all such numbers alpha 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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https://doi.org/10.5802/jtnb.1145View
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