On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909740246761472 |
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| author | Das, Sourabhashis Kuo, Wentang Liu, Yu-Ru |
| author_facet | Das, Sourabhashis Kuo, Wentang Liu, Yu-Ru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid Das, Sourabhashis Kuo, Wentang Liu, Yu-Ru Number Theory 11N80, 11K65, 20M32 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. |
| title | On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid |
| topic | Number Theory 11N80, 11K65, 20M32 |
| url | https://arxiv.org/abs/2508.12648 |