The inverse sieve problem in high dimensions
arXiv:1105.1551 · doi:10.1215/00127094-1645788
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.
arXiv comment15 pages. Added more examples in Section 5 and some minor changes