Friable averages of complex arithmetic functions

Régis de la Bretèche, Gérald Tenenbaum

Abstract: We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some complex power of the Riemann zeta function. We obtain asymptotic expansions resembling those provided by the Selberg-Delange method in the non-friable case. Some application are provided to the friable distribution of the additive function counting the total number of prime factors.

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution of integers with specified multiplicative constraints (11N25)

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