Additive functionals of Harmonic samples: the conditioned Dickman regime
Number Theory
2025-12-03 v1 Probability
Abstract
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type limits. This contrasts with the Gaussian limits of the classical Erd\"os-Kac theorem for uniform samples. Our perspective combines the probabilistic representation of harmonic samples via independent geometric variables with analytic inputs such as Mertens' approximation, together with a Poissonization procedure
Cite
@article{arxiv.2512.02926,
title = {Additive functionals of Harmonic samples: the conditioned Dickman regime},
author = {Victor Bernal Ramirez and Arturo Jaramillo},
journal= {arXiv preprint arXiv:2512.02926},
year = {2025}
}