Xuezhi Chen

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math.CA2024

Two-point polynomial patterns in subsets of positive density in $R^{n}$

Xuezhi Chen, Changxing Miao

Let $γ (t) = (P_{1} (t), \dots, P_{n} (t))$ where $P_{i}$ is a real polynomial with zero constant term for each $1 \leq i \leq n$ . We will show the existence of the configuration ${x, x + γ (t)}$ …

math.CA2023

A polynomial Roth theorem for corners in $R^{2}$ and a related bilinear singular integral operator

Xuezhi Chen, Jingwei Guo

We prove a quantitative Roth-type theorem for polynomial corners in $R^{2}$ . Let $P_{1}$ and $P_{2}$ be two linearly independent polynomials with zero constant term. We show tha…

math.CA2020

Two bipolynomial Roth theorems in $R$

Xuezhi Chen, Jingwei Guo, Xiaochun Li

We give two Roth theorems, related to the nonlinear configuration $x$ , $x + P_{1} (t)$ , $x + P_{2} (t)$ involving two polynomials, for sets in $R$ of positive density and of fractio…

Two-point polynomial patterns in subsets of positive density in Rn

A polynomial Roth theorem for corners in R2 and a related bilinear singular integral operator

Two bipolynomial Roth theorems in R

Two-point polynomial patterns in subsets of positive density in $R^{n}$

A polynomial Roth theorem for corners in $R^{2}$ and a related bilinear singular integral operator

Two bipolynomial Roth theorems in $R$