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arXiv · 1408.5043

The finiteness of computing the ultrametric Mahler measure

Charles L. Samuels
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Abstract

Recent work of Fili and the author examines an ultrametric version of the Mahler measure, denoted $M_\infty(α)$ for an algebraic number $α$. We show that the computation of $M_\infty(α)$ can be reduced to a certain search through a finite set. Although it is a open problem to record the points of this set in general, we provide some examples where it is reasonable to compute and our result can be used to determine $M_\infty(α)$.

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Charles L. Samuels. 2014-08-21. The finiteness of computing the ultrametric Mahler measure. https://doi.org/10.1142/s1793042110003745

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