Yu-Ru Liu · wovepaper

activity

20132025

most citedEquidistribution of polynomial sequences in function fields, with applications

5 citations · 6 across the 9 of their papers we have counts for

collaborators

10 papers

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

Jérémy Champagne, Zhenchao Ge, Thái Hoàng Lê +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…

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 $Ω (m)$ denoting the total number of prime elements generating $m$ . We study the moments of $Ω(\mat…

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

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $ω (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1940, Erdős and Kac established that $ω (n)$ obeys the Gaussian distribution over natural numbers.…

Generalizations of Erdős-Kac theorem with applications

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $ω (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1940, Erdős and Kac established that $ω (n)$ obeys the Gaussian distribution over natural numbers,…

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…

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 $ω_{k} (n)$ denote the number of distinct prime factors of $n$ with multiplicity $k$ as studied by Elma and the third author. We obtain asympto…

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

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

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

math.NT2024★ 1 cited

On the number of irreducible factors with a given multiplicity in function fields

Sourabhashis Das, Ertan Elma, Wentang Kuo +1

Let $k \geq 1$ be a natural number and $f \in F_{q} [t]$ be a monic polynomial. Let $ω_{k} (f)$ denote the number of distinct monic irreducible factors of $f$ with multiplicity…

Sieve Methods in Random Graph Theory

Yu-Ru Liu, J. C. Saunders

In this paper, we apply the Turan sieve and the simple sieve developed by R. Murty and the first author to study problems in random graph theory. In particular, we obtain upper and…

math.NT2013★ 5 cited

Equidistribution of polynomial sequences in function fields, with applications

Thái Hoàng Lê, Yu-Ru Liu, Trevor D. Wooley

We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greate…