• The inverse sieve problem in h...

Result: The inverse sieve problem in high dimensions

Title:
The inverse sieve problem in high dimensions
Authors:
Walsh, Miguel N.
Source:
CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
Duke Math. J. 161, no. 10 (2012), 2001-2022
Publication Status:
Preprint
Publisher Information:
Duke University Press, 2012.
Publication Year:
2012
Subject Terms:
11B30, Mathematics - Number Theory, Sieve Theory, 01 natural sciences, 11N69, Arithmetic Combinatorics, Inverse Sieve Problem, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, 11B30, 11N35, 11N35, Polynomial Method
Document Type:
Academic journal Article<br />Other literature type
File Description:
application/pdf
ISSN:
0012-7094
DOI:
10.1215/00127094-1645788
DOI:
10.48550/arxiv.1105.1551
Access URL:
http://arxiv.org/pdf/1105.1551
http://arxiv.org/abs/1105.1551
https://arxiv.org/abs/1105.1551
https://arxiv.org/pdf/1105.1551
http://ui.adsabs.harvard.edu/abs/2011arXiv1105.1551W/abstract
https://projecteuclid.org/journals/duke-mathematical-journal/volume-161/issue-10/The-inverse-sieve-problem-in-high-dimensions/10.1215/00127094-1645788.full
https://dialnet.unirioja.es/servlet/articulo?codigo=3971599
http://hdl.handle.net/11336/68296
http://projecteuclid.org/euclid.dmj/1340801630
Rights:
arXiv Non-Exclusive Distribution
CC BY NC SA
Accession Number:
edsair.doi.dedup.....b69991aff7fe0d304c303dcc3da1a44c
Database:
OpenAIRE

Further Information

We show that if a big set of integer points in [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.
15 pages. Added more examples in Section 5 and some minor changes