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arXiv · 2202.06287

Sur le biais d'une loi de probabilit\'e relative aux entiers friables

Gérald Tenenbaum
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Abstract

The standard probability law on the set $S(x,y)$ of $y$-friable integers not exceeding $x$ assigns to each friable integer $n$ a probability proportional to $1/n^\alpha$ where $\alpha=\alpha(x,y)$ is the saddle-point of the inverse Laplace integral for $\Psi(x,y):=|S(x,y)|$. This law presents a structural bias inasmuch it weights integers $>x$. We propose a quantitative measure of this bias and exhibit a related Gaussian distribution.

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Gérald Tenenbaum. 2022-02-13. Sur le biais d'une loi de probabilit\'e relative aux entiers friables. https://arxiv.org/abs/2202.06287

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