Geodesic
Mahler measures in a cubic field
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 949-956 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We prove that every cyclic cubic extension $E$ of the field of rational numbers contains algebraic numbers which are Mahler measures but not the Mahler measures of algebraic numbers lying in $E$. This extends the result of Schinzel who proved the same statement for every real quadratic field $E$. A corresponding conjecture is made for an arbitrary non-totally complex field $E$ and some numerical examples are given. We also show that every natural power of a Mahler measure is a Mahler measure.
We prove that every cyclic cubic extension $E$ of the field of rational numbers contains algebraic numbers which are Mahler measures but not the Mahler measures of algebraic numbers lying in $E$. This extends the result of Schinzel who proved the same statement for every real quadratic field $E$. A corresponding conjecture is made for an arbitrary non-totally complex field $E$ and some numerical examples are given. We also show that every natural power of a Mahler measure is a Mahler measure.
Classification : 11R06, 11R09, 11R16
Keywords: Mahler measure; Pisot numbers; cubic extension 
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Dubickas, Artūras. Mahler measures in a cubic field. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 949-956. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a12/

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