The inverse sieve problem in high dimensions (original) (raw)
15 July 2012 The inverse sieve problem in high dimensions
Miguel N. Walsh
Duke Math. J. 161(10): 2001-2022 (15 July 2012). DOI: 10.1215/00127094-1645788
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.
Citation
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
Information
Published: 15 July 2012
First available in Project Euclid: 27 June 2012
Digital Object Identifier: 10.1215/00127094-1645788
Subjects:
Primary: 11N35
Secondary: 11B30, 11N69
Rights: Copyright © 2012 Duke University Press
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Vol.161 • No. 10 • 15 July 2012
