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Original Articles

Constantes de Turán–Kubilius friables: une étude numérique

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Pages 345-361 | Received 04 Jun 2009, Accepted 03 Aug 2009, Published online: 11 Feb 2011
 

Abstract

This study is a follow-up to two recent works: [La Bretèche et Tenenbaum 05] and [Martin et Tenenbaum 10]. The former provides a friable (i.e., with respect to integers free of large prime factors) extension of the classical Turán–Kubilius inequality, while the latter furnishes a theoretical method for sharp evaluation of the involved constants. Here, we complement these investigations with a numerical study of the friable Turán–Kubilius constants, thereby supplying an effective, quantitative measure of the discrepancy between probabilistic number theory and its probabilistic model.

Cette étude fait suite à deux travaux récents: [La Bretèche et Tenenbaum 05] et [Martin et Tenenbaum 10]. Le premier fournit une extension friable (i.e., relative aux entiers sans grand facteur premier) de l'inégalité classique de Turán–Kubilius, tandis que le second propose une méthode théorique pour déterminer les constantes optimales impliquées. Ici, nous complétons ces recherches par une étude numérique des constantes friables de Turán–Kubilius, fournissant ainsi une mesure effective et quantitative de la discrépance entre la théorie probabiliste des nombres et son modèle probabiliste.

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