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 while it remains larger than a strictly positive constant when 2(1−ɛ)k > logy.
À la mémoire de Wolfgang Schwarz,
pour la délicatesse et la distinction
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de la Bretèche, R., Tenenbaum, G. (2016). Localisation Conditionnelle de Diviseurs. In: Sander, J., Steuding, J., Steuding, R. (eds) From Arithmetic to Zeta-Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-28203-9_3
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DOI: https://doi.org/10.1007/978-3-319-28203-9_3
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