Heights on Groups and Small Multiplicative Dependencies
Number Theory
2012-11-22 v1 Functional Analysis
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.
Cite
@article{arxiv.1211.5066,
title = {Heights on Groups and Small Multiplicative Dependencies},
author = {Jeffrey D. Vaaler},
journal= {arXiv preprint arXiv:1211.5066},
year = {2012}
}
Comments
28 pages