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

2025/08/18 by Das, Sourabhashis, Kuo, Wentang, Liu, Yu-Ru
#11K65 #11N80 #20M32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.12648

Abstract

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

Citations

• Generalizations of Erdős-Kac theorem with applications
• On the distribution of the number of distinct generators of h-free and h-full elements in an abelian monoid
• On the number of prime factors with a given multiplicity over h-free and h-full numbers

Related

• On the distribution of the number of distinct generators of h-free and h-full elements in an abelian monoid
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• Generalizations of Erdős-Kac theorem with applications
• On the number of prime factors with a given multiplicity over h-free and h-full numbers
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