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arXiv · 0808.1038

A Banach space determined by the Weil height

Daniel Allcock·Jeffrey D. Vaaler
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Abstract

The absolute logarithmic Weil height is well defined on the group of units of the algebraic closure of the rational numbers, modulo roots of unity, and induces a metric topology on this group. We show that the completion of this metric space is a Banach space over the field of real numbers. We further show that this Banach space is isometrically isomorphic to a co-dimension one subspace of L1 of a certain totally disconnected, locally compact space, equipped with a certain measure satisfying an invariance property with respect to the absolute Galois group.

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Daniel Allcock, Jeffrey D. Vaaler. 2008-08-07. A Banach space determined by the Weil height. https://doi.org/10.4064/aa136-3-6

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