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.
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}
}