@article{c1adcc29f77140e583db8c59b93e4ef1,
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 = "Funding Information: 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 ). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = jul,
day = "15",
doi = "10.1016/j.jfa.2021.109024",
language = "English (US)",
volume = "281",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "2",
}