Wentang Kuo

collaborators

7 papers

math.NT2025

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

Let $m$ be an element of an abelian monoid, with $I^c ◯ (m)$ denoting the total number of prime elements generating $m$ . We study the moments of $Î©(\m…

math.NT2025

A subset generalization of the ErdÅs-Kac theorem over number fields with applications

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $I ¨ (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1940, ErdÅs and Kac established that $I ¨ (n)$ obeys the Gaussian distribution over natural numbe…

math.NT2025

Generalizations of ErdÅs-Kac theorem with applications

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $I ¨ (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1940, ErdÅs and Kac established that $I ¨ (n)$ obeys the Gaussian distribution over natural numbe…

math.NT2025

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

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

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 st…

math.NT2024

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

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $k$ and $n$ be natural numbers. Let $I ¨ _{k} (n)$ denote the number of distinct prime factors of $n$ with multiplicity $k$ as studied by Elma and the third author. We obtain asympt…

math.NT2024

Distribution of $I ¨ (n)$ over $h$ -free and $h$ -full numbers

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $I ¨ (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1917, Hardy and Ramanujan proved that $I ¨ (n)$ has normal order $lo g lo g n$ over naturals. In t…

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

A subset generalization of the ErdÅs-Kac theorem over number fields with applications

Generalizations of ErdÅs-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

Distribution of I¨(n) over h-free and h-full numbers

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

A subset generalization of the ErdÅs-Kac theorem over number fields with applications

Generalizations of ErdÅs-Kac theorem with applications

Distribution of $I ¨ (n)$ over $h$ -free and $h$ -full numbers