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arXiv · 1508.01969

Heights, Regulators and Schinzel's determinant inequality

Shabnam Akhtari·Jeffrey D. Vaaler
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Abstract

We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension of number fields.

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Shabnam Akhtari, Jeffrey D. Vaaler. 2015-08-08. Heights, Regulators and Schinzel's determinant inequality. https://arxiv.org/abs/1508.01969

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