Transfinite diameter and the resultant
Complex Variables
2007-05-23 v1 Dynamical Systems
Number Theory
Abstract
We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E in C^N by a regular polynomial map F, expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F.
Cite
@article{arxiv.math/0601109,
title = {Transfinite diameter and the resultant},
author = {Laura DeMarco and Robert Rumely},
journal= {arXiv preprint arXiv:math/0601109},
year = {2007}
}