We show that if a big set of integer points , , occupies few residue classes mod for many primes , then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh.
Miguel N. Walsh. "The inverse sieve problem in high dimensions." Duke Math. J. 161 (10) 2001 - 2022, 15 July 2012. https://doi.org/10.1215/00127094-1645788