Arithmetic progressions of four squares over quadratic fields

Let d be a squarefree integer. Does there exist four squares in arithmeti progression over Q( √ d)? We shall give a partial answer to this question, depending on the value of d. In the a rmative ase, we onstru t expli it arithmeti progressions onsisting of four squares over Q( √ d)

Detalhes bibliográficos
Autores: González Jiménez, Enrique, Steiding, Jörn
Formato: artículo
Fecha de publicación:2018
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/711214
Acesso em linha:http://hdl.handle.net/10486/711214
https://dx.doi.org/10.48550/arXiv.0903.3856
Access Level:acceso abierto
Palavra-chave:Rank of Data
Congruent Numbers
Selmer Group
Matemáticas
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spelling Arithmetic progressions of four squares over quadratic fieldsGonzález Jiménez, EnriqueSteiding, JörnRank of DataCongruent NumbersSelmer GroupMatemáticasLet d be a squarefree integer. Does there exist four squares in arithmeti progression over Q( √ d)? We shall give a partial answer to this question, depending on the value of d. In the a rmative ase, we onstru t expli it arithmeti progressions onsisting of four squares over Q( √ d)Research of the first author was supported in part by grant MTM 2009-07291 (Ministerio de Educación y Ciencia, Spain) and CCG08- UAM/ESP–3906 (Universidad Autónoma de Madrid – Comunidad de Madrid, Spain). Research of the second author was supported in part by grant MTM 2006-01859 (Ministerio de Educación y Ciencia, Spain)Institute of Mathematics, University of DebrecenDepartamento de MatemáticasFacultad de Ciencias20182018-11-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/711214https://dx.doi.org/10.48550/arXiv.0903.3856reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7112142026-06-23T12:46:27Z
dc.title.none.fl_str_mv Arithmetic progressions of four squares over quadratic fields
title Arithmetic progressions of four squares over quadratic fields
spellingShingle Arithmetic progressions of four squares over quadratic fields
González Jiménez, Enrique
Rank of Data
Congruent Numbers
Selmer Group
Matemáticas
title_short Arithmetic progressions of four squares over quadratic fields
title_full Arithmetic progressions of four squares over quadratic fields
title_fullStr Arithmetic progressions of four squares over quadratic fields
title_full_unstemmed Arithmetic progressions of four squares over quadratic fields
title_sort Arithmetic progressions of four squares over quadratic fields
dc.creator.none.fl_str_mv González Jiménez, Enrique
Steiding, Jörn
author González Jiménez, Enrique
author_facet González Jiménez, Enrique
Steiding, Jörn
author_role author
author2 Steiding, Jörn
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Rank of Data
Congruent Numbers
Selmer Group
Matemáticas
topic Rank of Data
Congruent Numbers
Selmer Group
Matemáticas
description Let d be a squarefree integer. Does there exist four squares in arithmeti progression over Q( √ d)? We shall give a partial answer to this question, depending on the value of d. In the a rmative ase, we onstru t expli it arithmeti progressions onsisting of four squares over Q( √ d)
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-11-01
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
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 http://hdl.handle.net/10486/711214
https://dx.doi.org/10.48550/arXiv.0903.3856
url http://hdl.handle.net/10486/711214
https://dx.doi.org/10.48550/arXiv.0903.3856
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.publisher.none.fl_str_mv Institute of Mathematics, University of Debrecen
publisher.none.fl_str_mv Institute of Mathematics, University of Debrecen
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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