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Transfinite diameter and the resultant

Laura DeMarco·Robert Rumely
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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.

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Laura DeMarco, Robert Rumely. 2006-01-05. Transfinite diameter and the resultant. https://arxiv.org/abs/math/0601109

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