Open Access
2014 Metric heights on an Abelian group
Charles L. Samuels
Rocky Mountain J. Math. 44(6): 2075-2091 (2014). DOI: 10.1216/RMJ-2014-44-6-2075


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. "Metric heights on an Abelian group." Rocky Mountain J. Math. 44 (6) 2075 - 2091, 2014.


Published: 2014
First available in Project Euclid: 2 February 2015

zbMATH: 1306.11084
MathSciNet: MR3310962
Digital Object Identifier: 10.1216/RMJ-2014-44-6-2075

Primary: 11R04 , 11R09 , 20K99
Secondary: 26A06 , 30D20

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.44 • No. 6 • 2014
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