On primitive elements of finite fields avoiding affine hyperplanes

Abstract

Let n≥2 be an integer and let Fq be the finite field with q elements, where q is a prime power. Given Fq-affine hyperplanes A1,…,An of Fqn in general position, we study the existence and distribution of primitive elements of Fqn, avoiding each Ai. We obtain both asymptotic and concrete results, relating to past works on digits over finite fields.