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

2025/06/01 by Sourabhashis Das, Wentang Kuo, Das, Sourabhashis +3 · 1 citation
Computer Science · Mathematics · #11K65 #11N80 #20M32 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Probability (math.PR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2506.01030

openalex publication_date 2025/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work introduces the first in-depth study of h-free and h-full elements in abelian monoids, providing a unified approach for understanding their role in various mathematical structures. Let m be an element of an abelian monoid, with ω(m) denoting the number of distinct prime elements generating m. We study the moments of ω(m) over subsets of h-free and h-full elements, establishing the normal order of ω(m) within these subsets. Our findings are then applied to number fields, global function fields, and geometrically irreducible projective varieties, demonstrating the broad relevance of this approach.

Citations

• On the number of prime factors with a given multiplicity over h-free and h-full numbers

Cited by

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

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