English

The algebraicity of ill-distributed sets

Number Theory 2013-09-10 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.1307.0259,
  title  = {The algebraicity of ill-distributed sets},
  author = {Miguel N. Walsh},
  journal= {arXiv preprint arXiv:1307.0259},
  year   = {2013}
}

Comments

8 pages

R2 v1 2026-06-22T00:43:17.839Z