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.
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