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Abstract:

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.

Registro:

Documento: Artículo
Título:Nilsson solutions for irregular A-hypergeometric systems
Autor:Dickenstein, A.; Martínez, F.N.; Matusevich, L.F.
Filiación:Departamento de Matemática, FCEN, Universidad de Buenos Aires, C1428EGA Buenos Aires, Argentina
Department of Mathematics, Texas A and M University, College Station, TX 77843-3368, United States
Palabras clave:A-hypergeometric functions; Formal Nilsson series; Gröbner degenerations in the Weyl algebra; Irregular holonomic D-modules
Año:2012
Volumen:28
Número:3
Página de inicio:723
Página de fin:758
DOI: http://dx.doi.org/10.4171/rmi/689
Título revista:Revista Matematica Iberoamericana
Título revista abreviado:Rev. Mat. Iberoam.
ISSN:02132230
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v28_n3_p723_Dickenstein

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Citas:

---------- APA ----------
Dickenstein, A., Martínez, F.N. & Matusevich, L.F. (2012) . Nilsson solutions for irregular A-hypergeometric systems. Revista Matematica Iberoamericana, 28(3), 723-758.
http://dx.doi.org/10.4171/rmi/689
---------- CHICAGO ----------
Dickenstein, A., Martínez, F.N., Matusevich, L.F. "Nilsson solutions for irregular A-hypergeometric systems" . Revista Matematica Iberoamericana 28, no. 3 (2012) : 723-758.
http://dx.doi.org/10.4171/rmi/689
---------- MLA ----------
Dickenstein, A., Martínez, F.N., Matusevich, L.F. "Nilsson solutions for irregular A-hypergeometric systems" . Revista Matematica Iberoamericana, vol. 28, no. 3, 2012, pp. 723-758.
http://dx.doi.org/10.4171/rmi/689
---------- VANCOUVER ----------
Dickenstein, A., Martínez, F.N., Matusevich, L.F. Nilsson solutions for irregular A-hypergeometric systems. Rev. Mat. Iberoam. 2012;28(3):723-758.
http://dx.doi.org/10.4171/rmi/689