On the average distribution of divisors of friable numbers

Abstract

A number is said to be [Formula: see text]-friable if it has no prime factor greater than [Formula: see text]. In this paper, we prove a central limit theorem on average for the distribution of divisors of [Formula: see text]-friable numbers less than [Formula: see text], for all [Formula: see text] satisfying [Formula: see text]. This was previously known under the additional constraint [Formula: see text], by work of Basquin. Our argument relies on the two-variable saddle-point method.