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Canonical Heights, Transfinite Diameters, and Polynomial Dynamics | | Matthew Baker
; Liang-Chung Hsia
; | | Date: |
13 May 2003 | | Subject: | Number Theory; Dynamical Systems | math.NT math.DS | | Abstract: | Let phi(z) be a polynomial of degree at least 2 with coefficients in a number field K. Iterating phi gives rise to a dynamical system and a corresponding canonical height function, as defined by Call and Silverman. We prove a simple product formula relating the transfinite diameters of the filled Julia sets of phi 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. | | Source: | arXiv, math.NT/0305181 | | Services: | Forum | Review | PDF | Favorites | |
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