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arXiv · 2508.12648

On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid

Sourabhashis Das·Wentang Kuo·Yu-Ru Liu
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Abstract

Let $\mathfrak{m}$ be an element of an abelian monoid, with $\Omega(\mathfrak{m})$ denoting the total number of prime elements generating $\mathfrak{m}$. We study the moments of $\Omega(\mathfrak{m})$ over subsets of $h$-free and $h$-full elements, establishing the normal order of $\Omega(\mathfrak{m})$ 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.

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Sourabhashis Das, Wentang Kuo, Yu-Ru Liu. 2025-08-18. On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid. https://arxiv.org/abs/2508.12648

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