Yu-Ru Liu

collaborators

5 papers

math.NT2026

Equidistribution of polynomial sequences in function fields: resolution of a conjecture

JÃ©rÃ©my Champagne, Zhenchao Ge, ThÃ¡i HoÃ ng LÃª +2

Let $F_{q}$ be the finite field of $q$ elements having characteristic $p$ , and denote by $K_{\infty} = F_{q} ((1/ t))$ the field of formal Laurent series in $1/ t$ . We…

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…

Equidistribution of polynomial sequences in function fields: resolution of a conjecture

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 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