The inverse Sieve problem in high dimensions

Autores
Walsh, Miguel Nicolás
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Walsh, Miguel Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Sieve Theory
Arithmetic Combinatorics
Inverse Sieve Problem
Polynomial Method
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/68296
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/68296
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The inverse Sieve problem in high dimensionsWalsh, Miguel NicolásSieve TheoryArithmetic CombinatoricsInverse Sieve ProblemPolynomial Methodhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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.Fil: Walsh, Miguel Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaDuke University Press2012-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68296Walsh, Miguel Nicolás; The inverse Sieve problem in high dimensions; Duke University Press; Duke Mathematical Journal; 161; 10; 7-2012; 2001-20220012-7094CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.dmj/1340801630info:eu-repo/semantics/altIdentifier/doi/10.1215/00127094-1645788info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:20:44Zoai:ri.conicet.gov.ar:11336/68296instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:20:44.917CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The inverse Sieve problem in high dimensions
title The inverse Sieve problem in high dimensions
spellingShingle The inverse Sieve problem in high dimensions
Walsh, Miguel Nicolás
Sieve Theory
Arithmetic Combinatorics
Inverse Sieve Problem
Polynomial Method
title_short The inverse Sieve problem in high dimensions
title_full The inverse Sieve problem in high dimensions
title_fullStr The inverse Sieve problem in high dimensions
title_full_unstemmed The inverse Sieve problem in high dimensions
title_sort The inverse Sieve problem in high dimensions
dc.creator.none.fl_str_mv Walsh, Miguel Nicolás
author Walsh, Miguel Nicolás
author_facet Walsh, Miguel Nicolás
author_role author
dc.subject.none.fl_str_mv Sieve Theory
Arithmetic Combinatorics
Inverse Sieve Problem
Polynomial Method
topic Sieve Theory
Arithmetic Combinatorics
Inverse Sieve Problem
Polynomial Method
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Walsh, Miguel Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description 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.
publishDate 2012
dc.date.none.fl_str_mv 2012-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/68296
Walsh, Miguel Nicolás; The inverse Sieve problem in high dimensions; Duke University Press; Duke Mathematical Journal; 161; 10; 7-2012; 2001-2022
0012-7094
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68296
identifier_str_mv Walsh, Miguel Nicolás; The inverse Sieve problem in high dimensions; Duke University Press; Duke Mathematical Journal; 161; 10; 7-2012; 2001-2022
0012-7094
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.dmj/1340801630
info:eu-repo/semantics/altIdentifier/doi/10.1215/00127094-1645788
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Duke University Press
publisher.none.fl_str_mv Duke University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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