On a problem of Sárközy and Sós for multivariate linear forms

We prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes constant for n large enough. This result is a particular case of our main theorem,...

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Detalles Bibliográficos
Autores: Rué Perna, Juan José|||0000-0002-6420-3179, Spiegel, Christoph
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/121761
Acceso en línea:https://hdl.handle.net/2117/121761
https://dx.doi.org/10.1016/j.endm.2018.06.018
Access Level:acceso abierto
Palabra clave:Combinatorial analysis
additive combinatorics
representation functions
additive basis
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
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repository_id_str
spelling On a problem of Sárközy and Sós for multivariate linear formsRué Perna, Juan José|||0000-0002-6420-3179Spiegel, ChristophCombinatorial analysisadditive combinatoricsrepresentation functionsadditive basisAnàlisi combinatòriaÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::CombinatòriaWe prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes constant for n large enough. This result is a particular case of our main theorem, which poses a further step towards answering a question of S´ark¨ozy and S´os and widely extends a previous result of Cilleruelo and Ru´e for bivariate linear forms (Bull. of the London Math. Society 2009).20182018-07-0120182018-10-02journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/121761https://dx.doi.org/10.1016/j.endm.2018.06.018reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1217612026-05-27T15:37:01Z
dc.title.none.fl_str_mv On a problem of Sárközy and Sós for multivariate linear forms
title On a problem of Sárközy and Sós for multivariate linear forms
spellingShingle On a problem of Sárközy and Sós for multivariate linear forms
Rué Perna, Juan José|||0000-0002-6420-3179
Combinatorial analysis
additive combinatorics
representation functions
additive basis
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
title_short On a problem of Sárközy and Sós for multivariate linear forms
title_full On a problem of Sárközy and Sós for multivariate linear forms
title_fullStr On a problem of Sárközy and Sós for multivariate linear forms
title_full_unstemmed On a problem of Sárközy and Sós for multivariate linear forms
title_sort On a problem of Sárközy and Sós for multivariate linear forms
dc.creator.none.fl_str_mv Rué Perna, Juan José|||0000-0002-6420-3179
Spiegel, Christoph
author Rué Perna, Juan José|||0000-0002-6420-3179
author_facet Rué Perna, Juan José|||0000-0002-6420-3179
Spiegel, Christoph
author_role author
author2 Spiegel, Christoph
author2_role author
dc.subject.none.fl_str_mv Combinatorial analysis
additive combinatorics
representation functions
additive basis
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
topic Combinatorial analysis
additive combinatorics
representation functions
additive basis
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
description We prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes constant for n large enough. This result is a particular case of our main theorem, which poses a further step towards answering a question of S´ark¨ozy and S´os and widely extends a previous result of Cilleruelo and Ru´e for bivariate linear forms (Bull. of the London Math. Society 2009).
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-07-01
2018
2018-10-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/121761
https://dx.doi.org/10.1016/j.endm.2018.06.018
url https://hdl.handle.net/2117/121761
https://dx.doi.org/10.1016/j.endm.2018.06.018
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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