On the distribution of rational functions along a curve over Fp and residue races

Let p be a prime number, let F¯p be the algebraic closure of Fp=Z/pZ, let C be an absolutely irreducible curve in Ar(F¯p) and h=(h1,…,hs) a rational map defined on the curve C. We investigate the distribution in the s-dimensional unit cube (R/Z)s of the images through h of the Fp-points of C, after a suitable embedding.