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arXiv · 1211.5066

Heights on Groups and Small Multiplicative Dependencies

Jeffrey D. Vaaler
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Abstract

We generalize the absolute logarithmic Weil height from elements of the multiplicative group of algebraic numbers modulo torsion, to finitely generated subgoups. The height of a finitely generated subgroup is shown to equal the volume of a certain naturally occurring, convex, symmetric subset of Euclidean space. This connection leads to a bound on the norm of integer vectors that give multiplicative dependencies among finite sets of algebraic numbers.

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Jeffrey D. Vaaler. 2012-11-21. Heights on Groups and Small Multiplicative Dependencies. https://arxiv.org/abs/1211.5066

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