A generalized hermite constant for imaginary quadratic fields

Autores
Chan, Wai Kiu; Icaza, María Inés; Lauret, Emilio Agustin
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants coincide when K has class number one. Using the geometric tools developed by Mendoza and Vogtmann for their study of the homology of the Bianchi groups, we compute the projective Hermite constants for those K whose absolute discriminants are less than 70, and determine the hermitian forms that attain the projective Hermite constants in these cases. A comparison of the projective hermitian constant with some other generalizations of the classical Hermite constant is also given.
Fil: Chan, Wai Kiu. Wesleyan University; Estados Unidos
Fil: Icaza, María Inés. Universidad de Talca; Chile
Fil: Lauret, Emilio Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Extreme Hermitian Forms
Hermite Constant
Minima of Hermitian Forms
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:11336/51828
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A generalized hermite constant for imaginary quadratic fieldsChan, Wai KiuIcaza, María InésLauret, Emilio AgustinExtreme Hermitian FormsHermite ConstantMinima of Hermitian Formshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants coincide when K has class number one. Using the geometric tools developed by Mendoza and Vogtmann for their study of the homology of the Bianchi groups, we compute the projective Hermite constants for those K whose absolute discriminants are less than 70, and determine the hermitian forms that attain the projective Hermite constants in these cases. A comparison of the projective hermitian constant with some other generalizations of the classical Hermite constant is also given.Fil: Chan, Wai Kiu. Wesleyan University; Estados UnidosFil: Icaza, María Inés. Universidad de Talca; ChileFil: Lauret, Emilio Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaAmerican Mathematical Society2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/51828Chan, Wai Kiu; Icaza, María Inés; Lauret, Emilio Agustin; A generalized hermite constant for imaginary quadratic fields; American Mathematical Society; Mathematics Of Computation; 84; 294; 1-2015; 1883-19000025-5718CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2015-02903-2info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2015-84-294/S0025-5718-2015-02903-2/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:01:09Zoai:ri.conicet.gov.ar:11336/51828instacron: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:34982025-09-03 10:01:09.779CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A generalized hermite constant for imaginary quadratic fields
title A generalized hermite constant for imaginary quadratic fields
spellingShingle A generalized hermite constant for imaginary quadratic fields
Chan, Wai Kiu
Extreme Hermitian Forms
Hermite Constant
Minima of Hermitian Forms
title_short A generalized hermite constant for imaginary quadratic fields
title_full A generalized hermite constant for imaginary quadratic fields
title_fullStr A generalized hermite constant for imaginary quadratic fields
title_full_unstemmed A generalized hermite constant for imaginary quadratic fields
title_sort A generalized hermite constant for imaginary quadratic fields
dc.creator.none.fl_str_mv Chan, Wai Kiu
Icaza, María Inés
Lauret, Emilio Agustin
author Chan, Wai Kiu
author_facet Chan, Wai Kiu
Icaza, María Inés
Lauret, Emilio Agustin
author_role author
author2 Icaza, María Inés
Lauret, Emilio Agustin
author2_role author
author
dc.subject.none.fl_str_mv Extreme Hermitian Forms
Hermite Constant
Minima of Hermitian Forms
topic Extreme Hermitian Forms
Hermite Constant
Minima of Hermitian Forms
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants coincide when K has class number one. Using the geometric tools developed by Mendoza and Vogtmann for their study of the homology of the Bianchi groups, we compute the projective Hermite constants for those K whose absolute discriminants are less than 70, and determine the hermitian forms that attain the projective Hermite constants in these cases. A comparison of the projective hermitian constant with some other generalizations of the classical Hermite constant is also given.
Fil: Chan, Wai Kiu. Wesleyan University; Estados Unidos
Fil: Icaza, María Inés. Universidad de Talca; Chile
Fil: Lauret, Emilio Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants coincide when K has class number one. Using the geometric tools developed by Mendoza and Vogtmann for their study of the homology of the Bianchi groups, we compute the projective Hermite constants for those K whose absolute discriminants are less than 70, and determine the hermitian forms that attain the projective Hermite constants in these cases. A comparison of the projective hermitian constant with some other generalizations of the classical Hermite constant is also given.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/51828
Chan, Wai Kiu; Icaza, María Inés; Lauret, Emilio Agustin; A generalized hermite constant for imaginary quadratic fields; American Mathematical Society; Mathematics Of Computation; 84; 294; 1-2015; 1883-1900
0025-5718
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51828
identifier_str_mv Chan, Wai Kiu; Icaza, María Inés; Lauret, Emilio Agustin; A generalized hermite constant for imaginary quadratic fields; American Mathematical Society; Mathematics Of Computation; 84; 294; 1-2015; 1883-1900
0025-5718
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2015-02903-2
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2015-84-294/S0025-5718-2015-02903-2/
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 13.13397

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