On the Non-archimedean Metric Mahler Measure
نویسندگان
چکیده
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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