The algebraicity of ill-distributed sets

2013/07/01 by Miguel N. Walsh, Walsh, Miguel N.
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1307.0259

8 pages

arxiv created 2013/09/09 · arxiv updated 2013/09/10

Abstract

We show that every set S in [N]^d occupying less than p^t residue classes for some real number t < d and every prime p, must essentially lie in the solution set of a polynomial equation of degree at most (log N)^C, for some constant C depending only on t and d. This provides the first structural result for arbitrary t < d and S.

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