The probability that two random integers are coprime

Julien Bureaux (1) , Nathanaël Enriquez (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

An equivalence is proven between the Riemann Hypothesis and the speed of convergence to 1/zeta(2) of the probability that two independent random variables following the same geometric distribution are coprime integers, when the parameter of the distribution goes to 0.

Domaines: Probabilités [math.PR]

Julien Bureaux, Nathanaël Enriquez. The probability that two random integers are coprime. 2016. ⟨hal-01413829⟩