Geometric and Functional Analysis

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

The Algebraicity of Ill-Distributed Sets

  • Miguel N. Walsh


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.


Characteristic Subset Residue Class Integer Point Integer Parameter Inverse Theorem 
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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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