An application of the Hasse--Weil bound to rational functions over finite fields

Résumé fourni par la source

We use the Aubry–Perret bound for singular curves, a generalization of the Hasse–Weil bound, to prove the following curious result about rational functions over finite fields: Let $f(X),g(X)\in \Bbb F_q(X) \setminus \Bbb F_q$ be such that $q$ is sufficien