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∈k(z) of degree
>1 and a rational
function
a∈k(z) 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
