Distribution asymptotique des valeurs propres des endomorphismes de Frobenius [d'apr\`es Abel, Chebyshev, Robinson, ...]

Abstract

We consider unitary polynomials $P \in Z[X]$ whose roots $(x_i)$ belong to a given compact $K$ of $C$. To such a polynomial we associate the measure $\mu_P$ on $K$ which is the mean value of the Dirac measures $\delta_{x_i}$. What are the limits of the measures $\mu_P$ when $P$ varies ? In particular, what are their supports? We give partial answers to such questions, especially when $K$ is contained in $R$.