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arXiv · 1211.1890

Metric Heights on an Abelian Group

Charles L. Samuels
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Abstract

Suppose $m(\alpha)$ denotes the Mahler measure of the non-zero algebraic number $\alpha$. For each positive real number $t$, the author studied a version $m_t(\alpha)$ of the Mahler measure that has the triangle inequality. The construction of $m_t$ is generic, and may be applied to a broader class of functions defined on any Abelian group $G$. We prove analogs of known results with an abstract function on $G$ in place of the Mahler measure. In the process, we resolve an earlier open problem stated by the author regarding $m_t(\alpha)$.

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Charles L. Samuels. 2012-11-08. Metric Heights on an Abelian Group. https://doi.org/10.1216/rmj-2014-44-6-2075

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