Propriétés statistiques des entiers friables

@article{Bretche2005PropritsSD,
  title={Propri{\'e}t{\'e}s statistiques des entiers friables},
  author={R{\'e}gis de la Bret{\`e}che and Gerald Tenenbaum},
  journal={The Ramanujan Journal},
  year={2005},
  volume={9},
  pages={139-202}
}
Let Ψ(x,y) (resp. Ψm(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψm(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which… CONTINUE READING

Citations

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ON ULTRAFRIABLE INTEGERS

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CITES BACKGROUND & RESULTS

Nicolaas Govert de Bruijn, the enchanter of friable integers

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CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

On a paper of K. Soundararajan on smooth numbers in arithmetic progressions

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CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Une autre question concernant les friables translatés et étudiée par Fouvry et Tenenbaum

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HIGHLY INFLUENCED

Sommes friables de fonctions multiplicatives aléatoires

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CITES BACKGROUND
HIGHLY INFLUENCED

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