English

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

R2 v1 2026-06-21T21:17:52.095Z