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arXiv · 1408.4165

The infimum in the metric Mahler measure

Charles L. Samuels
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Abstract

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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Charles L. Samuels. 2014-08-18. The infimum in the metric Mahler measure. https://doi.org/10.4153/cmb-2011-028-x

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