Geodesic
The Infimum in the Metric Mahler Measure
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 739-747

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Dubickas and Smyth defined the metric Mahler measure on the multiplicative group of non-zero algebraic numbers. The definition involves taking an infimum over representations of an algebraic number $\alpha $ by other algebraic numbers. We verify their conjecture that the infimum in its definition is always achieved, and we establish its analog for the ultrametric Mahler measure.
DOI : 10.4153/CMB-2011-028-x
Mots-clés : 11R04, 11R09, Weil height, Mahler measure, metric Mahler measure, Lehmer's problem 
Samuels, Charles L. The Infimum in the Metric Mahler Measure. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 739-747. doi: 10.4153/CMB-2011-028-x
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     title = {The {Infimum} in the {Metric} {Mahler} {Measure}},
     journal = {Canadian mathematical bulletin},
     pages = {739--747},
     year = {2011},
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     number = {4},
     doi = {10.4153/CMB-2011-028-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-028-x/}
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