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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19955
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T09:47:25Zoai: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:34982025-09-03 09:47:25.317CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.13397 |