Analysis & PDE

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

On polynomial configurations in fractal sets

Kevin Henriot, Izabella Łaba, and Malabika Pramanik

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Abstract

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

(x,x + A1y,,x + Ak1y,x + Aky + Q(y)en),x n,y m,

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
Received: 25 November 2015
Revised: 29 March 2016
Accepted: 29 April 2016
First available in Project Euclid: 12 December 2017

Permanent link to this document
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
Secondary: 28A80: Fractals [See also 37Fxx]

Keywords
configurations in fractals additive combinatorics

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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