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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Detalles Bibliográficos
Autores principales:	Dickenstein, A., Martínez, F.N., Matusevich, L.F.
Formato:	JOUR
Materias:	A-hypergeometric functions Formal Nilsson series Gröbner degenerations in the Weyl algebra Irregular holonomic D-modules
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_02132230_v28_n3_p723_Dickenstein
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_02132230_v28_n3_p723_Dickenstein
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spelling	todo:paper_02132230_v28_n3_p723_Dickenstein2023-10-03T15:10:05Z Nilsson solutions for irregular A-hypergeometric systems Dickenstein, A. Martínez, F.N. Matusevich, L.F. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, A. Martínez, F.N. Matusevich, L.F. 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.
format	JOUR
author	Dickenstein, A. Martínez, F.N. Matusevich, L.F.
author_facet	Dickenstein, A. Martínez, F.N. Matusevich, L.F.
author_sort	Dickenstein, A.
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
url	http://hdl.handle.net/20.500.12110/paper_02132230_v28_n3_p723_Dickenstein
work_keys_str_mv	AT dickensteina nilssonsolutionsforirregularahypergeometricsystems AT martinezfn nilssonsolutionsforirregularahypergeometricsystems AT matusevichlf nilssonsolutionsforirregularahypergeometricsystems
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Nilsson solutions for irregular A-hypergeometric systems

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