Guoqing Zhan

collaborators

3 papers

math.CA2026

Boundedness of Multilinear Hilbert Transforms Along Moment Curves

Jingwei Guo, Xiaochun Li, Guoqing Zhan

We prove the boundedness of multilinear Hilbert transforms along moment curves by establishing uniform estimates for both translated and untranslated multilinear paraproducts and b…

math.NT2026

A multidimensional Szemerédi theorem in integers

Jingwei Guo, Changxing Miao, Guoqing Zhan

For any integer $n \geq 2$ , let $(m_{1}, \dots, m_{n})$ be a strictly increasing $n$ -tuple of positive integers. We show that any subset $A \subset [N]^{n}$ of density at least $(\log…

math.CA2025

Improvement of Pólya's conjecture for balls and cylinders

Jingwei Guo, Changxing Miao, Weiwei Wang +1

Pólya's conjecture on the eigenvalues of the Laplacian has been one of the core problems in spectral geometry. Building upon the recent breakthrough works on Pólya's conjecture for…