Lehmer points and visible points on affine varieties over finite fields

Kit-Ho Mak; Alexandru Zaharescu

doi:10.1017/S0305004113000613

Lehmer points and visible points on affine varieties over finite fields

Number Theory 2019-02-20 v4 Algebraic Geometry

Authors: Kit-Ho Mak , Alexandru Zaharescu

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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.

Keywords

Lehmer points visible points affine varieties finite fields congruence conditions asymptotic results

Cite

@article{arxiv.1110.4691,
  title  = {Lehmer points and visible points on affine varieties over finite fields},
  author = {Kit-Ho Mak and Alexandru Zaharescu},
  journal= {arXiv preprint arXiv:1110.4691},
  year   = {2019}
}

Comments

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

Lehmer points and visible points on affine varieties over finite fields

Abstract

Keywords

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