Zeta functions of the 3-dimensional almost-Bieberbach groups

Autores
Sulca, Diego Armando
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group can be expressed as finite sums of Dirichlet series admitting Euler product factorization. We compute these series except for a finite number of local factors when the group is virtually nilpotent of Hirsch length 3. We deduce that they can be meromorphically continued to the whole complex plane and that they satisfy local functional equations. The complete computation (with no exception of local factors) is presented for those groups that are also torsion-free, that is, for the 3-dimensional almost-Bieberbach groups.
Fil: Sulca, Diego Armando. 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
ZETA FUNCTIONS
SUBGROUP GROWTH
ALMOST-BIEBERBACH GROUPS
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:11336/217372
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Zeta functions of the 3-dimensional almost-Bieberbach groupsSulca, Diego ArmandoZETA FUNCTIONSSUBGROUP GROWTHALMOST-BIEBERBACH GROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group can be expressed as finite sums of Dirichlet series admitting Euler product factorization. We compute these series except for a finite number of local factors when the group is virtually nilpotent of Hirsch length 3. We deduce that they can be meromorphically continued to the whole complex plane and that they satisfy local functional equations. The complete computation (with no exception of local factors) is presented for those groups that are also torsion-free, that is, for the 3-dimensional almost-Bieberbach groups.Fil: Sulca, Diego Armando. 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; ArgentinaDe Gruyter2022-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/217372Sulca, Diego Armando; Zeta functions of the 3-dimensional almost-Bieberbach groups; De Gruyter; Journal Of Group Theory; 25; 4; 1-2022; 601-6781433-5883CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/jgth-2021-0072info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:10:23Zoai:ri.conicet.gov.ar:11336/217372instacron: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:34982025-09-10 13:10:23.561CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Zeta functions of the 3-dimensional almost-Bieberbach groups
title Zeta functions of the 3-dimensional almost-Bieberbach groups
spellingShingle Zeta functions of the 3-dimensional almost-Bieberbach groups
Sulca, Diego Armando
ZETA FUNCTIONS
SUBGROUP GROWTH
ALMOST-BIEBERBACH GROUPS
title_short Zeta functions of the 3-dimensional almost-Bieberbach groups
title_full Zeta functions of the 3-dimensional almost-Bieberbach groups
title_fullStr Zeta functions of the 3-dimensional almost-Bieberbach groups
title_full_unstemmed Zeta functions of the 3-dimensional almost-Bieberbach groups
title_sort Zeta functions of the 3-dimensional almost-Bieberbach groups
dc.creator.none.fl_str_mv Sulca, Diego Armando
author Sulca, Diego Armando
author_facet Sulca, Diego Armando
author_role author
dc.subject.none.fl_str_mv ZETA FUNCTIONS
SUBGROUP GROWTH
ALMOST-BIEBERBACH GROUPS
topic ZETA FUNCTIONS
SUBGROUP GROWTH
ALMOST-BIEBERBACH GROUPS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group can be expressed as finite sums of Dirichlet series admitting Euler product factorization. We compute these series except for a finite number of local factors when the group is virtually nilpotent of Hirsch length 3. We deduce that they can be meromorphically continued to the whole complex plane and that they satisfy local functional equations. The complete computation (with no exception of local factors) is presented for those groups that are also torsion-free, that is, for the 3-dimensional almost-Bieberbach groups.
Fil: Sulca, Diego Armando. 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 The subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group can be expressed as finite sums of Dirichlet series admitting Euler product factorization. We compute these series except for a finite number of local factors when the group is virtually nilpotent of Hirsch length 3. We deduce that they can be meromorphically continued to the whole complex plane and that they satisfy local functional equations. The complete computation (with no exception of local factors) is presented for those groups that are also torsion-free, that is, for the 3-dimensional almost-Bieberbach groups.
publishDate 2022
dc.date.none.fl_str_mv 2022-01
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/11336/217372
Sulca, Diego Armando; Zeta functions of the 3-dimensional almost-Bieberbach groups; De Gruyter; Journal Of Group Theory; 25; 4; 1-2022; 601-678
1433-5883
CONICET Digital
CONICET
url http://hdl.handle.net/11336/217372
identifier_str_mv Sulca, Diego Armando; Zeta functions of the 3-dimensional almost-Bieberbach groups; De Gruyter; Journal Of Group Theory; 25; 4; 1-2022; 601-678
1433-5883
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/jgth-2021-0072
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/zip
application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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 12.993085

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