Equidistribution and generalized Mahler measures

Details Equidistribution and generalized Mahler measures Equidistribution and generalized Mahler measures

2005-10-19

arxiv.org/abs/math/0510404v3

Mathematics

Number Theory

29 pages

Scientific paper

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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