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Propriétés multiplicatives des entiers friables translatés

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Drappeau S.

Colloquium Mathematicum

2014

tom 137

nr 2

149-164

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.

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1 Colloquium Mathematicum

1 Drappeau S.

1 2014

Wyniki wyszukiwania

Propriétés multiplicatives des entiers friables translatés