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Localisation Conditionnelle de Diviseurs

In: From Arithmetic to Zeta-Functions

Author

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  • Régis de la Bretèche

    (Université Paris Diderot-Paris 7, Institut de Mathématiques de Jussieu-PRG, UMR 7586
    Institut de Mathématiques de Jussieu-PRG, UMR 7586)

  • Gérald Tenenbaum

    (Université de Lorraine, Institut Élie Cartan)

Abstract

In support of a still little known, general principle according to which the structure of the set of prime factors of an integer is statistically governed by its actual cardinal, we show that, given any ɛ > 0, the conditional probability that an integer with exactly k prime factors has a divisor in a dyadic interval ]y, 2y] approaches 0 as y → ∞ if 2(1+ɛ)k logy.

Suggested Citation

  • Régis de la Bretèche & Gérald Tenenbaum, 2016. "Localisation Conditionnelle de Diviseurs," Springer Books, in: Jürgen Sander & Jörn Steuding & Rasa Steuding (ed.), From Arithmetic to Zeta-Functions, pages 41-55, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28203-9_3
    DOI: 10.1007/978-3-319-28203-9_3
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