On the Non-archimedean Metric Mahler Measure

  title={On the Non-archimedean Metric Mahler Measure},
  author={Paul Fili},
Recently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metric näıve height on the multiplicative group of algebraic numbers. We give a non-Archimedean version of the metric Mahler measure, denoted M∞, and prove that M∞(α) = 1 if and only if α is a root of unity. We further show that M∞ defines a projective height on Q × /Tor(Q) as a vector space over Q. Finally, we demonstrate how to compute M∞(α) when α is a surd. 

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