\(k\)-point configurations in sets of positive density of \(\mathbb{Z}^n\)

DOI10.1215/00127094-2008-060zbMath1165.05029OpenAlexW2011065523MaRDI QIDQ2518252

Ákos Magyar

Publication date: 15 January 2009

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/00127094-2008-060

zbMATH Keywords

geometric Ramsey theory

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Ramsey theory (05D10)

Related Items

Multilinear maximal operators associated to simplices ⋮ Finite configurations in sparse sets ⋮ Density theorems for anisotropic point configurations ⋮ Discrete maximal operators over surfaces of higher codimension ⋮ Weak hypergraph regularity and applications to geometric Ramsey theory ⋮ The sovability of norm, bilinear and quadratic equations over finite fields via spectra of graphs ⋮ A Furstenberg-Katznelson-Weiss type theorem on \((d+1)\)-point configurations in sets of positive density in finite field geometries ⋮ Pinned distance sets, \(k\)-simplices, Wolff's exponent in finite fields and sum-product estimates ⋮ Simplices over finite fields ⋮ Ubiquity of simplices in subsets of vector spaces over finite fields ⋮ Patterns in sets of positive density in trees and affine buildings

Cites Work

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• Modular forms of degree \(n\) and representation by quadratic forms
• On distance sets of large sets of integer points
• Lectures on Siegel modular forms and representation by quadratic forms
• A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\)
• An ergodic Szemerédi theorem for commuting transformations
• On the theory of indefinite quadratic forms

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