Zeta functions of singular curves over finite fields

Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let ς (X,t) be its zeta function [Ser1], If X is a singular curve, two other zeta functions exist. The first is the Dirichlet series Z(Ca(X), t) associated to the effective Cartier divisors on X; the s...

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Autores:
Zúñiga Galindo, Wilson Alvaro
Tipo de recurso:
Article of journal
Fecha de publicación:
1997
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/43675
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/43675
http://bdigital.unal.edu.co/33773/
Palabra clave:
Zeta functions
finite fields
singular curves
generalized Jacobians
compactified Jacobians
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/43675
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network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Zúñiga Galindo, Wilson Alvarodb235a38-2db6-48de-9fb3-ed4aa245582b3002019-06-28T12:17:40Z2019-06-28T12:17:40Z1997https://repositorio.unal.edu.co/handle/unal/43675http://bdigital.unal.edu.co/33773/Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let ς (X,t) be its zeta function [Ser1], If X is a singular curve, two other zeta functions exist. The first is the Dirichlet series Z(Ca(X), t) associated to the effective Cartier divisors on X; the second is the Dirichlet series Z(Div(X),t) associated to the effective divisors on X, In this paper we generalize F. K. Schmidt's results on the rationality and functional equation of the zeta function ς(X, t) of a non-singular curve to the functions Z(Ca(X), t) and Z(Div(X), t) by means ofthe singular Riemann-Roch theorem.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/33674Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 31, núm. 2 (1997); 115-124 0034-7426Zúñiga Galindo, Wilson Alvaro (1997) Zeta functions of singular curves over finite fields. Revista Colombiana de Matemáticas; Vol. 31, núm. 2 (1997); 115-124 0034-7426 .Zeta functions of singular curves over finite fieldsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTZeta functionsfinite fieldssingular curvesgeneralized Jacobianscompactified JacobiansORIGINAL33674-125557-1-PB.pdfapplication/pdf4001388https://repositorio.unal.edu.co/bitstream/unal/43675/1/33674-125557-1-PB.pdf350f69dc5ceea9adb6682bda0527823eMD51THUMBNAIL33674-125557-1-PB.pdf.jpg33674-125557-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6826https://repositorio.unal.edu.co/bitstream/unal/43675/2/33674-125557-1-PB.pdf.jpg818e861220201bf0a5ab2d4732e0b4b3MD52unal/43675oai:repositorio.unal.edu.co:unal/436752024-02-11 23:18:50.108Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Zeta functions of singular curves over finite fields
title Zeta functions of singular curves over finite fields
spellingShingle Zeta functions of singular curves over finite fields
Zeta functions
finite fields
singular curves
generalized Jacobians
compactified Jacobians
title_short Zeta functions of singular curves over finite fields
title_full Zeta functions of singular curves over finite fields
title_fullStr Zeta functions of singular curves over finite fields
title_full_unstemmed Zeta functions of singular curves over finite fields
title_sort Zeta functions of singular curves over finite fields
dc.creator.fl_str_mv Zúñiga Galindo, Wilson Alvaro
dc.contributor.author.spa.fl_str_mv Zúñiga Galindo, Wilson Alvaro
dc.subject.proposal.spa.fl_str_mv Zeta functions
finite fields
singular curves
generalized Jacobians
compactified Jacobians
topic Zeta functions
finite fields
singular curves
generalized Jacobians
compactified Jacobians
description Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let ς (X,t) be its zeta function [Ser1], If X is a singular curve, two other zeta functions exist. The first is the Dirichlet series Z(Ca(X), t) associated to the effective Cartier divisors on X; the second is the Dirichlet series Z(Div(X),t) associated to the effective divisors on X, In this paper we generalize F. K. Schmidt's results on the rationality and functional equation of the zeta function ς(X, t) of a non-singular curve to the functions Z(Ca(X), t) and Z(Div(X), t) by means ofthe singular Riemann-Roch theorem.
publishDate 1997
dc.date.issued.spa.fl_str_mv 1997
dc.date.accessioned.spa.fl_str_mv 2019-06-28T12:17:40Z
dc.date.available.spa.fl_str_mv 2019-06-28T12:17:40Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/33773/
url https://repositorio.unal.edu.co/handle/unal/43675
http://bdigital.unal.edu.co/33773/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/33674
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 31, núm. 2 (1997); 115-124 0034-7426
dc.relation.references.spa.fl_str_mv Zúñiga Galindo, Wilson Alvaro (1997) Zeta functions of singular curves over finite fields. Revista Colombiana de Matemáticas; Vol. 31, núm. 2 (1997); 115-124 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
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dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
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dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
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