The inverse sieve problem in high dimensions
Number Theory
2019-12-19 v2
Abstract
We show that if a big set of integer points in [0,N]^d, d>1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh.
Cite
@article{arxiv.1105.1551,
title = {The inverse sieve problem in high dimensions},
author = {Miguel N. Walsh},
journal= {arXiv preprint arXiv:1105.1551},
year = {2019}
}
Comments
15 pages. Added more examples in Section 5 and some minor changes