## Analysis & PDE

• Anal. PDE
• Volume 9, Number 5 (2016), 1153-1184.

### On polynomial configurations in fractal sets

#### Abstract

We show that subsets of $ℝn$ of large enough Hausdorff and Fourier dimension contain polynomial patterns of the form

$(x,x + A1y,…,x + Ak−1y,x + Aky + Q(y)en),x ∈ ℝn,y ∈ ℝm,$

where $Ai$ are real $n × m$ matrices, $Q$ is a real polynomial in $m$ variables and $en = (0,…,0,1)$.

#### Article information

Source
Anal. PDE, Volume 9, Number 5 (2016), 1153-1184.

Dates
Revised: 29 March 2016
Accepted: 29 April 2016
First available in Project Euclid: 12 December 2017

https://projecteuclid.org/euclid.apde/1513097070

Digital Object Identifier
doi:10.2140/apde.2016.9.1153

Mathematical Reviews number (MathSciNet)
MR3531369

Zentralblatt MATH identifier
06608422

Subjects
Primary: 11B30: Arithmetic combinatorics; higher degree uniformity

#### Citation

Henriot, Kevin; Łaba, Izabella; Pramanik, Malabika. On polynomial configurations in fractal sets. Anal. PDE 9 (2016), no. 5, 1153--1184. doi:10.2140/apde.2016.9.1153. https://projecteuclid.org/euclid.apde/1513097070

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