Propriétés multiplicatives des entiers friables translatés

• Autorzy: Sary Drappeau
• Języki publikacji: FR EN

Abstrakty

EN

An integer n is said to be y-friable if its greatest prime factor P(n) is less than y. In this paper, we study numbers of the shape n-1 when P(n) ≤ y and n ≤ x. One expects that, statistically, their multiplicative behaviour resembles that of all integers less than x. Extending a result of Basquin (2010), we estimate the mean value over shifted friable numbers of certain arithmetic functions when $(log x^{c}) ≤ y$ for some positive c, showing a change in behaviour according to whether log y/log x tends to infinity or not. In the same range in (x, y), we prove an Erdős-Kac-type theorem for shifted friable numbers, improving a result of Fouvry & Tenenbaum (1996). The results presented here are obtained using recent work of Harper (2012) on the statistical distribution of friable numbers in arithmetic progressions.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11N25: Distribution of integers with specified multiplicative constraints

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 2
• Strony: 149-164

Daty

wydano

2014

Twórcy

autor

Sary Drappeau

• Centre de recherches mathématiques, Université de Montréal, CP 6128, succ. Centre-Ville, Montréal H3C 3J7, Canada

Identyfikatory

DOI

10.4064/cm137-2-1