Subgroups Generated by Rational Functions in Finite Fields

Abstract

For a large prime $p$, a rational function $\psi \in F_p(X)$ over the finite field $F_p$ of $p$ elements, and integers $u$ and $H\ge 1$, we obtain a lower bound on the number consecutive values $\psi (x)$, $x=u+1,\dots ,u+H$ that belong to a given multiplicative subgroup of $F_p^{\ast }$.

References in corpus (1)

• Points on curves in small boxes en applications