Lehmer points and visible points on affine varieties over finite fields

Abstract

Let $V$ be an absolutely irreducible affine variety over ${\mathbb{F}}_p$. A Lehmer point on $V$ is a point whose coordinates satisfy some prescribed congruence conditions, and a visible point is one whose coordinates are relatively prime. Asymptotic results for the number of Lehmer points and visible points on $V$ are obtained, and the distribution of visible points into different congruence classes is investigated.

16 pages, accepted for publication in Math. Proc. Cambridge Philos. Soc. Theorem 2 of this paper is improved from the published version