Nilsson solutions for irregular A-hypergeometric systems

We study the solutions of irregular A-hypergeometric systems that are constructed from Gröbner 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 serie...

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Autores principales: Dickenstein, Alicia Marcela, Martínez, Federico Nicolás
Publicado: 2012
Materias:
A-hypergeometric functions
Formal Nilsson series
Gröbner degenerations in the Weyl algebra
Irregular holonomic D-modules
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v28_n3_p723_Dickenstein
http://hdl.handle.net/20.500.12110/paper_02132230_v28_n3_p723_Dickenstein
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02132230_v28_n3_p723_Dickenstein
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spelling paper:paper_02132230_v28_n3_p723_Dickenstein2023-06-08T15:20:47Z Nilsson solutions for irregular A-hypergeometric systems Dickenstein, Alicia Marcela Martínez, Federico Nicolás A-hypergeometric functions Formal Nilsson series Gröbner degenerations in the Weyl algebra Irregular holonomic D-modules We study the solutions of irregular A-hypergeometric systems that are constructed from Gröbner 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 Cn. 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. © European Mathematical Society. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Martínez, F.N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v28_n3_p723_Dickenstein http://hdl.handle.net/20.500.12110/paper_02132230_v28_n3_p723_Dickenstein
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A-hypergeometric functions
Formal Nilsson series
Gröbner degenerations in the Weyl algebra
Irregular holonomic D-modules
spellingShingle A-hypergeometric functions
Formal Nilsson series
Gröbner degenerations in the Weyl algebra
Irregular holonomic D-modules
Dickenstein, Alicia Marcela
Martínez, Federico Nicolás
Nilsson solutions for irregular A-hypergeometric systems
topic_facet A-hypergeometric functions
Formal Nilsson series
Gröbner degenerations in the Weyl algebra
Irregular holonomic D-modules
description We study the solutions of irregular A-hypergeometric systems that are constructed from Gröbner 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 Cn. 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. © European Mathematical Society.
author Dickenstein, Alicia Marcela
Martínez, Federico Nicolás
author_facet Dickenstein, Alicia Marcela
Martínez, Federico Nicolás
author_sort Dickenstein, Alicia Marcela
title Nilsson solutions for irregular A-hypergeometric systems
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
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v28_n3_p723_Dickenstein
http://hdl.handle.net/20.500.12110/paper_02132230_v28_n3_p723_Dickenstein
work_keys_str_mv AT dickensteinaliciamarcela nilssonsolutionsforirregularahypergeometricsystems
AT martinezfedericonicolas nilssonsolutionsforirregularahypergeometricsystems
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