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 . The limit behaviour of this distribution as the side length of the random square tends to infinity is also considered.
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}
}