## An effective lower bound for the height of algebraic numbers.(English)Zbl 0838.11065

Let $$\alpha$$ be a non-zero algebraic number of degree $$d$$. We make effective the argument of Cantor and Straus to show that if $$\alpha$$ is not a root of unity and $$d\geq 2$$ then $$dh(\alpha)= \log M(\alpha)> (1/4) (\log (d)/ \log \log (d))^3$$, where $$h(\cdot)$$ denotes the absolute logarithmic height and $$M(\cdot)$$ denotes the Mahler measure. Some related corollaries are also given.

### MSC:

 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
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