## Duke Mathematical Journal

### The inverse sieve problem in high dimensions

Miguel N. Walsh

#### Abstract

We show that if a big set of integer points $S\subseteq[0,N]^{d}$, $d\textgreater 1$, 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.

#### Article information

Source
Duke Math. J., Volume 161, Number 10 (2012), 2001-2022.

Dates
First available in Project Euclid: 27 June 2012

https://projecteuclid.org/euclid.dmj/1340801630

Digital Object Identifier
doi:10.1215/00127094-1645788

Mathematical Reviews number (MathSciNet)
MR2954623

Zentralblatt MATH identifier
1357.11090

#### Citation

Walsh, Miguel N. The inverse sieve problem in high dimensions. Duke Math. J. 161 (2012), no. 10, 2001--2022. doi:10.1215/00127094-1645788. https://projecteuclid.org/euclid.dmj/1340801630

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