Nilsson solutions for irregular A-hypergeometric systems

Autores
Dickenstein, Alicia Marcela; Martinez, Federico Nicolas; Matusevich, Laura Felicia
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the solutions of irregular A-hypergeometric systems that are constructed from Grobner degenerations with respect to generic positive weight ¨ vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1, . . . , 1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of C n . Our results are more explicit when the parameters are generic or when the solutions studied are logarithm-free. We also give an alternative proof of a result of Schulze and Walther that inhomogeneous A-hypergeometric systems have irregular singularities.
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Martinez, Federico Nicolas. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Matusevich, Laura Felicia. Texas A&M University; Estados Unidos
Materia
Hypergeometric
Irregular
Nilsson Solution
Holonomic Rank
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:11336/19955
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Nilsson solutions for irregular A-hypergeometric systemsDickenstein, Alicia MarcelaMartinez, Federico NicolasMatusevich, Laura FeliciaHypergeometricIrregularNilsson SolutionHolonomic Rankhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the solutions of irregular A-hypergeometric systems that are constructed from Grobner degenerations with respect to generic positive weight ¨ vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1, . . . , 1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of C n . Our results are more explicit when the parameters are generic or when the solutions studied are logarithm-free. We also give an alternative proof of a result of Schulze and Walther that inhomogeneous A-hypergeometric systems have irregular singularities.Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martinez, Federico Nicolas. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Matusevich, Laura Felicia. Texas A&M University; Estados UnidosEuropean Mathematical Society2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19955Dickenstein, Alicia Marcela; Martinez, Federico Nicolas; Matusevich, Laura Felicia; Nilsson solutions for irregular A-hypergeometric systems; European Mathematical Society; Revista Matematica Iberoamericana; 28; 3; 2012; 723-7580213-2230CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4171/RMI/689info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=28&iss=3&rank=3info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1007.4225info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:28Zoai:ri.conicet.gov.ar:11336/19955instacron: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:34982025-09-29 09:39:28.49CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nilsson solutions for irregular A-hypergeometric systems
title Nilsson solutions for irregular A-hypergeometric systems
spellingShingle Nilsson solutions for irregular A-hypergeometric systems
Dickenstein, Alicia Marcela
Hypergeometric
Irregular
Nilsson Solution
Holonomic Rank
title_short Nilsson solutions for irregular A-hypergeometric systems
title_full Nilsson solutions for irregular A-hypergeometric systems
title_fullStr Nilsson solutions for irregular A-hypergeometric systems
title_full_unstemmed Nilsson solutions for irregular A-hypergeometric systems
title_sort Nilsson solutions for irregular A-hypergeometric systems
dc.creator.none.fl_str_mv Dickenstein, Alicia Marcela
Martinez, Federico Nicolas
Matusevich, Laura Felicia
author Dickenstein, Alicia Marcela
author_facet Dickenstein, Alicia Marcela
Martinez, Federico Nicolas
Matusevich, Laura Felicia
author_role author
author2 Martinez, Federico Nicolas
Matusevich, Laura Felicia
author2_role author
author
dc.subject.none.fl_str_mv Hypergeometric
Irregular
Nilsson Solution
Holonomic Rank
topic Hypergeometric
Irregular
Nilsson Solution
Holonomic Rank
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the solutions of irregular A-hypergeometric systems that are constructed from Grobner degenerations with respect to generic positive weight ¨ vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1, . . . , 1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of C n . Our results are more explicit when the parameters are generic or when the solutions studied are logarithm-free. We also give an alternative proof of a result of Schulze and Walther that inhomogeneous A-hypergeometric systems have irregular singularities.
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Martinez, Federico Nicolas. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Matusevich, Laura Felicia. Texas A&M University; Estados Unidos
description We study the solutions of irregular A-hypergeometric systems that are constructed from Grobner degenerations with respect to generic positive weight ¨ vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1, . . . , 1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of C n . Our results are more explicit when the parameters are generic or when the solutions studied are logarithm-free. We also give an alternative proof of a result of Schulze and Walther that inhomogeneous A-hypergeometric systems have irregular singularities.
publishDate 2012
dc.date.none.fl_str_mv 2012
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/11336/19955
Dickenstein, Alicia Marcela; Martinez, Federico Nicolas; Matusevich, Laura Felicia; Nilsson solutions for irregular A-hypergeometric systems; European Mathematical Society; Revista Matematica Iberoamericana; 28; 3; 2012; 723-758
0213-2230
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19955
identifier_str_mv Dickenstein, Alicia Marcela; Martinez, Federico Nicolas; Matusevich, Laura Felicia; Nilsson solutions for irregular A-hypergeometric systems; European Mathematical Society; Revista Matematica Iberoamericana; 28; 3; 2012; 723-758
0213-2230
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/RMI/689
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=28&iss=3&rank=3
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1007.4225
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
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European 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 13.069144

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