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arXiv · 1508.01726

Continued fraction expansions in connection with the metric Mahler measure

Charles L. Samuels
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Abstract

The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer's conjecture in topological language. More recent work of the author examined a parametrized family of generalized metric Mahler measures that gives rise to a series of new, and apparently difficult, problems. We establish a connection between these metric Mahler measures and the theory of continued fractions in a certain class of special cases. Our results enable us to calculate metric Mahler measures in several new examples.

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Charles L. Samuels. 2016-08-01. Continued fraction expansions in connection with the metric Mahler measure. https://doi.org/10.1007/s00605-016-0900-6

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