Zhuowen Guo

collaborators

4 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.DS2026

Perturbed Polynomial Powers and Bourgain Entropy Obstructions for Khintchin Averages

Zhuowen Guo, Shuhao Zhang

Let $a \geq 2$ , let $p \in Z [n]$ be eventually increasing and eventually non-negative, and let $I^»_{n} = a^{p (n)} + f (n) > 0$ , where $f (n) \in Z$ . We prove, using Bourgain's bou…

math.DS2026

Fractal transference principles for subsets of $N^{d}$ of positive density

Zhuowen Guo, Kangbo Ouyang, Jiahao Qiu +1

We establish a multidimensional fractal transference principle for digit-restricted sets associated with subsets of $N^{d}$ , extending the one-dimensional framework of Nakaj…

math.DS2026

On subsets of integers having dense orbits

Zhuowen Guo, Jiahao Qiu, Hui Xu +1

Let $A \subset N$ . We say $A$ is an $R$ -sequence for a given minimal system $(Y, S)$ if there is $y \in Y$ such that ${S^{n} y : n \in A}$ is dense in $Y$ . Richter asked if $A$ i…

A three-dimensional corner configuration involving the Omega function

Perturbed Polynomial Powers and Bourgain Entropy Obstructions for Khintchin Averages

Fractal transference principles for subsets of Nd of positive density

On subsets of integers having dense orbits

Fractal transference principles for subsets of $N^{d}$ of positive density