Two bipolynomial Roth theorems in R

Xuezhi Chen; Jingwei Guo; Xiaochun Li

doi:10.1016/j.jfa.2021.109024

Two bipolynomial Roth theorems in R

Xuezhi Chen, Jingwei Guo, Xiaochun Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give two Roth theorems, related to the nonlinear configuration x, x+P₁(t), x+P₂(t) involving two polynomials, for sets in R of positive density and of fractional dimensions. The proof uses Fourier analysis.

Original language	English (US)
Article number	109024
Journal	Journal of Functional Analysis
Volume	281
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2021.109024
State	Published - Jul 15 2021

Keywords

Bipolynomial
Fractional dimensions
Oscillatory integral
σ-Uniformity

ASJC Scopus subject areas

Analysis

Online availability

10.1016/j.jfa.2021.109024

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title = "Two bipolynomial Roth theorems in R",

abstract = "We give two Roth theorems, related to the nonlinear configuration x, x+P1(t), x+P2(t) involving two polynomials, for sets in R of positive density and of fractional dimensions. The proof uses Fourier analysis.",

keywords = "Bipolynomial, Fractional dimensions, Oscillatory integral, σ-Uniformity",

author = "Xuezhi Chen and Jingwei Guo and Xiaochun Li",

note = "J. G. is partially supported by the Fundamental Research Funds for the Central Universities (No. WK3470000013 ) and the NSFC Grant (No. 11571331 ). X. L. is supported by Simons fellowship in Math 2019-2020 (No. 617526 ).",

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AU - Guo, Jingwei

AU - Li, Xiaochun

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KW - Bipolynomial

KW - Fractional dimensions

KW - Oscillatory integral

KW - σ-Uniformity

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Two bipolynomial Roth theorems in R

Abstract

Keywords

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Online availability

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