A Banach space determined by the Weil height
Number Theory
2015-05-13 v1
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.
Cite
@article{arxiv.0808.1038,
title = {A Banach space determined by the Weil height},
author = {Daniel Allcock and Jeffrey D. Vaaler},
journal= {arXiv preprint arXiv:0808.1038},
year = {2015}
}