Equidistribution and generalized Mahler measures

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Let g be a nonconstant rational map from the projective line to itself that has degree greater than one and is defined over a number field. The map g gives rise to generalized Mahler measures for polynomials in one variable. We use diophantine approximation to show that the generalized Mahler measure of a polynomial F at a place v can be computed by averaging the log of the v-adic absolute value of F over the periodic points of g. This allows us to compute canonical heights of algebraic points via equidistribution on periodic points.
29 pages

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Number Theory, Dynamical Systems, 11G50; 11J68, 37F10

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http://salesiana.dossiersoluciones.com/handle/123456789/127099

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510404
 http://arxiv.org/abs/math/0510404

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arXiv