Equidistribution of the conjugates of algebraic units

Abstract

We prove an equidistribution result for the zeros of polynomials with integer coefficients and simple zeros. Specifically, we show that the normalized zero measures associated with a sequence of such polynomials, having small height relative to a certain compact set in the complex plane, converge to a canonical measure on the set. In particular, this result gives an equidistribution result for the conjugates of algebraic units, in the spirit of Bilu's work. Our approach involves lifting these polynomials to polynomial mappings in two variables and proving an equidistribution result for the normalized zero measures in this setting.