Additive functionals of Harmonic samples: the conditioned Dickman regime
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917119531155456 |
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| author | Ramirez, Victor Bernal Jaramillo, Arturo |
| author_facet | Ramirez, Victor Bernal Jaramillo, Arturo |
| contents | 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 Erdös-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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additive functionals of Harmonic samples: the conditioned Dickman regime Ramirez, Victor Bernal Jaramillo, Arturo Number Theory Probability 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 Erdös-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 |
| title | Additive functionals of Harmonic samples: the conditioned Dickman regime |
| topic | Number Theory Probability |
| url | https://arxiv.org/abs/2512.02926 |