2007•Journal für die reine und angewandte Mathematik (Crelles Journal)Requires access

Transfinite diameter and the resultant

Laura DeMarco, Robert S. Rumely

Abstract

We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂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 .

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Key concepts: Transfinite number, Pullback, Mathematics, Pure mathematics, Set (abstract data type), Polynomial, Key (lock), Algebra over a field