9 citations · 35 across the 12 of their papers we have counts for
13 papers
Two remarks on Narkiewicz's property (P)
Lukas Pottmeyer
Due to Narkiewicz a field has property (P) if for no polynomial of degree at least two there is an infinite -invariant subset of . We present a new example of…
Wandering points for the Mahler measure
Paul Fili, Lukas Pottmeyer, Mingming Zhang
Mahler's measure defines a dynamical system on the algebraic numbers. In this paper, we study the problem of which number fields have points which wander under the iteration of Mah…
On the behavior of Mahler's measure under iteration
Paul Fili, Lukas Pottmeyer, Mingming Zhang
For an algebraic number we denote by the Mahler measure of . As is again an algebraic number (indeed, an algebraic integer), is a self-map on $\over…
Fields Generated by Finite Rank Subgroups of
Lukas Pottmeyer
Let be a finite rank subgroup of . We prove that the multiplicative group of the field generated by all elements in the divisible hull of , is free…
Perfect powers in value sets and orbits of polynomials
Alina Ostafe, Lukas Pottmeyer, Igor E. Shparlinski
We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by…
Small totally -adic algebraic numbers
Lukas Pottmeyer
The purpose of this note is to give a short and elementary proof of the fact, that the absolute logarithmic Weil-height is bounded from below by a positive constant for all totally…
Quantitative height bounds under splitting conditions
Paul Fili, Lukas Pottmeyer
In an earlier work, the first author and Petsche used potential theoretic techniques to establish a lower bound for the height of algebraic numbers that satisfy splitting condition…
Heights and totally -adic numbers
Lukas Pottmeyer
We study the behavior of canonical height functions , associated to rational maps , on totally -adic fields. In particular, we prove that there is a gap betwee…
A note on extensions of
Lukas Pottmeyer
In this note we investigate the behaviour of the absolute logarithmic Weil-height h on extensions of the field of totally real numbers. It is known that there is…
Small points and free abelian groups
Robert Grizzard, Philipp Habegger, Lukas Pottmeyer
Let be an algebraic extension of the rational numbers and an elliptic curve defined over some number field contained in . The absolute logarithmic Weil height, respectiv…
Heights and totally real numbers
Lukas Pottmeyer
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…
Heights of points with bounded ramification
Lukas Pottmeyer
Let be an elliptic curve defined over a number field with fixed non-archimedean absolute value of split-multiplicative reduction, and let be an associated Lattès ma…
A Dynamical Bogomolov Property
Lukas Pottmeyer
A field F is said to have the Bogomolov Property related to a height function h, if h(a) is either zero or bounded from below by a positive constant for all a in F. In this paper w…