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The Infimum in the Metric Mahler Measure

Published online by Cambridge University Press:  20 November 2018

Charles L. Samuels
Charles L. Samuels*
Affiliation:
Simon Fraser University, Department of Mathematics, Burnaby, BC V5A 1S6, andUniversity of British Columbia, Department of Mathematics, Vancouver, BC V6T 1Z2e-mail: csamuels@sfu.ca
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Abstract

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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.

Keywords

11R0411R09Weil heightMahler measuremetric Mahler measureLehmer's problem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011 , pp. 739 - 747
Copyright
Copyright © Canadian Mathematical Society 2011

References

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