On arithmetic progressions on Edwards curves

Assume m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an 2 2 2 arithmetic progression in the Edwards curve Ed : x + y = 1 + d x2y . In these conditions, we study the set APm(a, q) and we parametrize it by the rational points o...

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Detalles Bibliográficos
Autor: González Jiménez, Enrique
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/711220
Acceso en línea:http://hdl.handle.net/10486/711220
https://dx.doi.org/10.4064/aa167-2-2
Access Level:acceso abierto
Palabra clave:Arithmetic Progression
Elliptic Curves
Edwards Curves
Matemáticas
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spelling On arithmetic progressions on Edwards curvesGonzález Jiménez, EnriqueArithmetic ProgressionElliptic CurvesEdwards CurvesMatemáticasAssume m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an 2 2 2 arithmetic progression in the Edwards curve Ed : x + y = 1 + d x2y . In these conditions, we study the set APm(a, q) and we parametrize it by the rational points of an algebraic curveWe would like to thank to Nils Bruin, Luis Dieulefait and Xevi Guitart for some interesting and useful discussions, and José M. Tornero, who read the earlier versions of this paper carefully. This research was partly supported by the grant MTM2012–35849Institute of MathematicsDepartamento de MatemáticasFacultad de Ciencias20142014-10-14research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/711220https://dx.doi.org/10.4064/aa167-2-2reponame: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:10486/7112202026-06-23T12:46:27Z
dc.title.none.fl_str_mv On arithmetic progressions on Edwards curves
title On arithmetic progressions on Edwards curves
spellingShingle On arithmetic progressions on Edwards curves
González Jiménez, Enrique
Arithmetic Progression
Elliptic Curves
Edwards Curves
Matemáticas
title_short On arithmetic progressions on Edwards curves
title_full On arithmetic progressions on Edwards curves
title_fullStr On arithmetic progressions on Edwards curves
title_full_unstemmed On arithmetic progressions on Edwards curves
title_sort On arithmetic progressions on Edwards curves
dc.creator.none.fl_str_mv González Jiménez, Enrique
author González Jiménez, Enrique
author_facet González Jiménez, Enrique
author_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Arithmetic Progression
Elliptic Curves
Edwards Curves
Matemáticas
topic Arithmetic Progression
Elliptic Curves
Edwards Curves
Matemáticas
description Assume m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an 2 2 2 arithmetic progression in the Edwards curve Ed : x + y = 1 + d x2y . In these conditions, we study the set APm(a, q) and we parametrize it by the rational points of an algebraic curve
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-10-14
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/10486/711220
https://dx.doi.org/10.4064/aa167-2-2
url http://hdl.handle.net/10486/711220
https://dx.doi.org/10.4064/aa167-2-2
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
publisher.none.fl_str_mv Institute of Mathematics
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
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repository.mail.fl_str_mv
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