Two bipolynomial Roth theorems in ℝ

2020/08/29 by Xuezhi Chen, Jingwei Guo, Chen, Xuezhi +3
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2008.13011

openalex publication_date 2020/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Non-Linear Roth Theorem for Fractals of Sufficiently Large Dimension

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