2005/10/19 by Lucien Szpiro, Szpiro, Lucien, Thomas J. Tucker +1
Mathematics · #11G50 #11J68 #37F10 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.math/0510404
openalex publication_date 2005/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.