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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2005, Issue 585


Canonical heights, transfinite diameters, and polynomial dynamics

Matthew H. Baker / Liang-Chung Hsia
Published Online: 2005-11-07 | DOI: https://doi.org/10.1515/crll.2005.2005.585.61


Let ϕ(z ) be a polynomial of degree at least 2 with coefficients in a number field K. Iterating ϕ gives rise to a dynamical system and a corresponding canonical height function ĥϕ , as defined by Call and Silverman. We prove a simple product formula relating the transfinite diameters of the filled Julia sets of ϕ over various completions of K, and we apply this formula to give a generalization of Bilu’s equidistribution theorem for sequences of points whose canonical heights tend to zero.

About the article

Published Online: 2005-11-07

Published in Print: 2005-08-26

Citation Information: Journal für die reine und angewandte Mathematik, Volume 2005, Issue 585, Pages 61–92, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crll.2005.2005.585.61.

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