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Equidistribution and generalized Mahler measures

Lucien Szpiro·Thomas J. Tucker
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Abstract

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.

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BibTeXRIS

Lucien Szpiro, Thomas J. Tucker. 2007-04-10. Equidistribution and generalized Mahler measures. https://arxiv.org/abs/math/0510404

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