Geodesic
Mahler measures in a cubic field
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 949-956

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMJ_2006__56_3_a12,
     author = {Dubickas, Art\={u}ras},
     title = {Mahler measures in a cubic field},
     journal = {Czechoslovak Mathematical Journal},
     pages = {949--956},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2006},
     mrnumber = {2261666},
     zbl = {1164.11068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006__56_3_a12/}
}
TY  - JOUR
AU  - Dubickas, Artūras
TI  - Mahler measures in a cubic field
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 949
EP  - 956
VL  - 56
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006__56_3_a12/
LA  - en
ID  - CMJ_2006__56_3_a12
ER  - 
%0 Journal Article
%A Dubickas, Artūras
%T Mahler measures in a cubic field
%J Czechoslovak Mathematical Journal
%D 2006
%P 949-956
%V 56
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2006__56_3_a12/
%G en
%F CMJ_2006__56_3_a12
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/