Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.12752 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914720074694656 |
|---|---|
| author | Fernández, José L. Fernández, Pablo |
| author_facet | Fernández, José L. Fernández, Pablo |
| contents | 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 $\mathbb{N}^2$. The limit behaviour of this distribution as the side length of the random square tends to infinity is also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting coprime pairs in random squares Fernández, José L. Fernández, Pablo Number Theory Probability 11K65, 11N36, 11A51 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 $\mathbb{N}^2$. The limit behaviour of this distribution as the side length of the random square tends to infinity is also considered. |
| title | Counting coprime pairs in random squares |
| topic | Number Theory Probability 11K65, 11N36, 11A51 |
| url | https://arxiv.org/abs/2403.12752 |