Canonical Heights, Transfinite Diameters, and Polynomial Dynamics

Details Canonical Heights, Transfinite Diameters, and Polynomial Dynamics Canonical Heights, Transfinite Diameters, and Polynomial Dynamics

2003-05-13

arxiv.org/abs/math/0305181v2

Mathematics

Number Theory

28 pages, revised version. Lemma 7.1 and Theorem 4.3 have been corrected, and Remark 7.3 and Corollary 8.3 have been added

Scientific paper

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.

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