On the average distribution of divisors of friable numbers

Abstract : A number is said to be y-friable if it has no prime factor greater than y. In this paper, we prove a central limit theorem on average for the distribution of divisors of y-friable numbers less than x, for all (x, y) satisfying 2 ≤ y ≤ e (log x)/(log log x) 1+ε. This was previously known under the additional constraint y ≥ e (log log x) 5/3+ε , by work of Basquin. Our argument relies on the two-variable saddle-point method.
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Sary Drappeau. On the average distribution of divisors of friable numbers. International Journal of Number Theory, World Scientific Publishing, 2017, 13 (01), pp.153 - 193. ⟨10.1142/S1793042117500105⟩. ⟨hal-01302600⟩

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