The inverse sieve problem in high dimensions
Miguel N. Walsh
Source: Duke Math. J. Volume 161, Number 10
(2012), 2001-2022.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1340801630
Digital Object Identifier: doi:10.1215/00127094-1645788
Zentralblatt MATH identifier: 06063227
Mathematical Reviews number (MathSciNet): MR2954623
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