Heights and totally real numbers

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.

Major changes regarding the first version. E.g. the last chapter was canceled

References in corpus (3)

• Small Height and Infinite Non-Abelian Extensions
• Global discrepancy and small points on elliptic curves
• Equidistribution and the heights of totally real and totally p-adic numbers

Cited by in corpus (1)

• Heights and totally $p$-adic numbers