Heights and totally real numbers
Number Theory
2013-11-19 v2 Dynamical Systems
Abstract
1973 Schinzel proved that the standard logarithmic height h on the maximal totally real field extension of the rationals is either zero or bounded from below by a positive constant. In this paper we study this property for canonical heights associated to rational functions and the corresponding dynamical system on the affine line. At the end, we will give a few remarks on the behavior of h on finite extensions of the maximal totally real field.
Keywords
Cite
@article{arxiv.1206.2456,
title = {Heights and totally real numbers},
author = {Lukas Pottmeyer},
journal= {arXiv preprint arXiv:1206.2456},
year = {2013}
}
Comments
Major changes regarding the first version. E.g. the last chapter was canceled