English

Friable averages of complex arithmetic functions

Number Theory 2024-07-23 v6

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.

Keywords

Cite

@article{arxiv.2305.06486,
  title  = {Friable averages of complex arithmetic functions},
  author = {Régis de la Bretèche and Gérald Tenenbaum},
  journal= {arXiv preprint arXiv:2305.06486},
  year   = {2024}
}
R2 v1 2026-06-28T10:31:34.614Z