Effective divisors on the projective line having small diagonals and small heights and their application to adelic dynamics

Yûsuke Okuyama

Vol. 280 (2016), No. 1, 141–175

DOI: 10.2140/pjm.2016.280.141

Abstract

We establish a quantitative adelic equidistribution theorem for a sequence of effective divisors on the projective line over the separable closure of a product formula field having small diagonals and small $g$-heights with respect to an adelic normalized weight $g$ in arbitrary characteristic and in a possibly nonseparable setting. Applying this quantitative adelic equidistribution result to adelic dynamics of $f$, we obtain local proximity estimates between the iterations of a rational function $f\in k\left(z\right)$ of degree $>1$ and a rational function $a\in k\left(z\right)$ of degree $>0$ over a product formula field $k$ of characteristic $0$.

Keywords

product formula field, effective divisor, small diagonals, small heights, quantitative equidistribution, asymptotically Fekete configuration, local proximity sequence, adelic dynamics

Mathematical Subject Classification 2010

Primary: 37P30

Secondary: 11G50, 37P50, 37F10

Milestones

Received: 29 July 2014

Revised: 5 April 2015

Accepted: 14 April 2015

Published: 28 December 2015