Multiplicative Partitions: A Unified Asymptotic Framework for Arbitrary Subsets over Arbitrary Scaled Intervals
Abstract
We study multiplicative partitions of integers restricted to a subset $\mathcal{S} \subseteq \mathbb{N} \setminus \{1\}$. Under explicit regular-variation hypotheses on the counting function $\pi_{\mathcal{S}}(x)$ (allowing base growth $\pi_{\mathcal{S}}(x)\asymp x^{\alpha}$ with arbitrary $0
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Combinatorial Mathematics
Limits and Structures in Graph Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 6 February 2026
- Document type
- Preprint