English

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.

Keywords

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

R2 v1 2026-06-21T18:04:17.802Z