Nilsson solutions for irregular A-hypergeometric systems Academic Article

abstract

• We study the solutions of irregular A-hypergeometric systems that are constructed from Grbner 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.

authors

• Matusevich, Laura

published proceedings

• REVISTA MATEMATICA IBEROAMERICANA

author list (cited authors)

• Dickenstein, A., Martinez, F. N., & Matusevich, L. F.

citation count

• 6

complete list of authors

• Dickenstein, Alicia||Martinez, Federico N||Matusevich, Laura Felicia

publication date

• December 2012

publisher

• European Mathematical Society - EMS - Publishing House GmbH  Publisher

published in

• Revista Matematica Iberoamericana  Journal

keywords

• A-hypergeometric Functions
• Formal Nilsson Series
• Grobner Degenerations In The Weyl Algebra
• Irregular Holonomic D-modules

Digital Object Identifier (DOI)

• 10.4171/RMI/689

start page

• 723

end page

• 758

volume

• 28

issue

• 3

URL

• http://dx.doi.org/10.4171/rmi/689