On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid
Year: 2025
Type: preprint
Abstract: Let $\mathfrak{m}$ be an element of an abelian monoid, with $Ω(\mathfrak{m})$ denoting the total number of prime elements generating $\mathfrak{m}$. We study the moments of $Ω(\mathfrak{m})$ over subsets of $h$-free and $h$-full elements, establishing the normal order of $Ω(\mathfrak{m})$ within these subsets. This work continues the study on the distribution of generalized arithmetic functions over $h$-free and $h$-full elements in abelian monoids as introduced in the authors' previous work.
Source: arXiv (Cornell University)
Authors: Das, Sourabhashis, Kuo, Wentang, Liu, Yu-Ru
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7076954344
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