English

Counting coprime pairs in random squares

Number Theory 2024-03-20 v1 Probability

Abstract

Extending the classical Dirichlet's density theorem on coprime pairs, in this paper we describe completely the probability distribution of the number of coprime pairs in random squares of fixed side length in the lattice N2\mathbb{N}^2. The limit behaviour of this distribution as the side length of the random square tends to infinity is also considered.

Keywords

Cite

@article{arxiv.2403.12752,
  title  = {Counting coprime pairs in random squares},
  author = {José L. Fernández and Pablo Fernández},
  journal= {arXiv preprint arXiv:2403.12752},
  year   = {2024}
}
R2 v1 2026-06-28T15:25:46.906Z