Duke Mathematical Journal

The inverse sieve problem in high dimensions

Miguel N. Walsh

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Abstract

We show that if a big set of integer points S[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.

Article information

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

Dates
First available in Project Euclid: 27 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1340801630

Digital Object Identifier
doi:10.1215/00127094-1645788

Mathematical Reviews number (MathSciNet)
MR2954623

Zentralblatt MATH identifier
1357.11090

Subjects
Primary: 11N35: Sieves
Secondary: 11B30: Arithmetic combinatorics; higher degree uniformity 11N69: Distribution of integers in special residue classes

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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