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arXiv · 1511.09305

On the average distribution of divisors of friable numbers

Sary Drappeau
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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 $2\leq y \leq {\rm e}^{(\log x)/(\log\log x)^{1+\varepsilon}}$. This was previously known under the additional constraint $y\geq {\rm e}^{(\log\log x)^{5/3+\varepsilon}}$, by work of Basquin. Our argument relies on the two-variable saddle-point method.

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Sary Drappeau. 2015-11-30. On the average distribution of divisors of friable numbers. https://doi.org/10.1142/s1793042117500105

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