Counting coprime pairs in random squares
- Resource Type
- Working Paper
- Authors
- Fernández, José L.; Fernández, Pablo
- Source
- Subject
- Mathematics - Number Theory
Mathematics - Probability
11K65, 11N36, 11A51
- Language
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.