Rongzhong Xiao

collaborators

5 papers

math.DS2026

A three-dimensional corner configuration involving the Omega function

Zhuowen Guo, Rongzhong Xiao, Shuhao Zhang

Let $Ω (n)$ denote the number of prime factors of $n$ , counted with multiplicity. We prove that if $A \subset N^{3}$ has positive upper Banach density, then there are $(x,y,z)\…

math.CO2026

An affirmative answer to Owings's sumset question

Wen Huang, Zhengxing Lian, Song Shao +3

We give an affirmative answer to Owings's sumset question: for any $2$ -coloring of natural numbers, there is an infinite $B \subseteq N$ such that $B + B$ is monochromatic. Mo…

math.DS2024

Some ergodic theorems involving Omega function and their applications

Rongzhong Xiao

In this paper, we build some ergodic theorems involving function $Ω$ , where $Ω (n)$ denotes the number of prime factors of a natural number $n$ counted with multiplicities. As a com…

math.CO2024

Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers

Wen Huang, Song Shao, Tianyi Tao +2

In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N^2 satisfy the sets {lambda x, lambda y, x y, lam…

math.CO2024

Monochromatic polynomial sumset structures on $N$

Zhengxing Lian, Rongzhong Xiao

In the paper, we search for monochromatic infinite additive structures involving polynomials over $N$ . It is proved that for any $r \in N$ , any two distinct natura…

A three-dimensional corner configuration involving the Omega function

An affirmative answer to Owings's sumset question

Some ergodic theorems involving Omega function and their applications

Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers

Monochromatic polynomial sumset structures on N

Monochromatic polynomial sumset structures on $N$