Lois de répartition des diviseurs des entiers friables

Sary Drappeau 1 Gérald Tenenbaum 2
2 Analyse
IECL - Institut Élie Cartan de Lorraine
Abstract : According to a general probabilistic principle, the natural divisors of friable integers (i.e.~free of large prime factors) should normally present a Gaussian distribution. We show that this indeed is the case with conditional density tending to 1 as soon as the standard necessary conditions are met. Furthermore, we provide explicit, essentially optimal estimates for the decay of the involved error terms. The size of the exceptional set is sufficiently small to enable recovery of the average behaviour in the same optimal range. Our argument combines the saddle-point method with new large deviations estimates for the distribution of certain additive functions.
Type de document :
Pré-publication, Document de travail
In French, English abstract. 2016
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https://hal.archives-ouvertes.fr/hal-01479205
Contributeur : Aigle I2m <>
Soumis le : mardi 28 février 2017 - 16:49:03
Dernière modification le : mercredi 1 mars 2017 - 13:01:40

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  • HAL Id : hal-01479205, version 1
  • ARXIV : 1604.04204

Citation

Sary Drappeau, Gérald Tenenbaum. Lois de répartition des diviseurs des entiers friables. In French, English abstract. 2016. <hal-01479205>

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