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dc.contributor.author
Sulca, Diego Armando
dc.date.available
2023-11-07T17:42:27Z
dc.date.issued
2022-01
dc.identifier.citation
Sulca, Diego Armando; Zeta functions of the 3-dimensional almost-Bieberbach groups; De Gruyter; Journal Of Group Theory; 25; 4; 1-2022; 601-678
dc.identifier.issn
1433-5883
dc.identifier.uri
http://hdl.handle.net/11336/217372
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
De Gruyter
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
ZETA FUNCTIONS
dc.subject
SUBGROUP GROWTH
dc.subject
ALMOST-BIEBERBACH GROUPS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Zeta functions of the 3-dimensional almost-Bieberbach groups
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-11-06T15:23:41Z
dc.journal.volume
25
dc.journal.number
4
dc.journal.pagination
601-678
dc.journal.pais
Alemania
dc.journal.ciudad
Berlin
dc.description.fil
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
dc.journal.title
Journal Of Group Theory
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1515/jgth-2021-0072
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