Transfinite diameter and the resultant

Laura DeMarco; Robert Rumely

doi:10.1515/CRELLE.2007.077

Transfinite diameter and the resultant

Laura DeMarco^*, Robert Rumely

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	145-161
Number of pages	17
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	611
DOIs	https://doi.org/10.1515/CRELLE.2007.077
State	Published - Oct 26 2007

Funding

The first author was supported in part by an NSF Postdoctoral Fellowship (DMS 0303421) and the second author by NSF grant DMS 0300784.

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/CRELLE.2007.077

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abstract = "We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E 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.",

author = "Laura DeMarco and Robert Rumely",

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AU - Rumely, Robert

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Y1 - 2007/10/26

N2 - We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E 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.

AB - We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E 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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Transfinite diameter and the resultant

Abstract

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ASJC Scopus subject areas

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