Distribution asymptotique des valeurs propres des endomorphismes de Frobenius [d'après 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 $R$.

arXiv comment42 pages, in French. 1 Figure. Bourbaki seminar March 2018, revised and completed. To appear in SMF, Astérisque, 2019. The new version contains two corrections suggested by J. Rivera-Letelier and M. Sombra. It differs from v2 by the suppression of section A.8, which was repeating section A.7