3 papers
math.NT2026
Poisson--Dirichlet approximation for counting integers with divisors in an interval
Tony Haddad
We give a simple inequality that compares the laws of two random variables taking values in a convex subset of a normed vector space. By combining this with Arratia's coupling, rec…
math.NT2025
On Arratia's coupling and the Dirichlet law for the factors of a random integer
Tony Haddad, Dimitris Koukoulopoulos
Let , let be an integer chosen uniformly at random from the set , and let be a Poisson--Dirichlet process of parameter $1…
math.NT2024
Visiting early at prime times
Tony Haddad, Sun-Kai Leung, Cihan Sabuncu
Given an integer and a sufficiently large , we apply a variant of the Maynard--Tao sieve weight to establish the existence of an arithmetic progression with common di…