Mathematics > Number Theory
[Submitted on 18 Aug 2014]
Title:The infimum in the metric Mahler measure
View PDFAbstract: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 as well as establish its analog for the ultrametric Mahler measure.
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