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Geometric and Functional Analysis

, Volume 24, Issue 3, pp 959–967 | Cite as

The Algebraicity of Ill-Distributed Sets

  • Miguel N. Walsh
Article

Abstract

We show that every set \({S \subseteq [N]^d}\) occupying \({\ll p^{\kappa}}\) residue classes for some real number \({0 \leq \kappa < d}\) and every prime p, must essentially lie in the solution set of a polynomial equation of degree \({\ll ({\rm log} N)^C}\), for some constant C depending only on \({\kappa}\) and d. This provides the first structural result for arbitrary \({\kappa < d}\) and S.

Keywords

Characteristic Subset Residue Class Integer Point Integer Parameter Inverse Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

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