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TitleNilsson solutions for irregular A-hypergeometric systems.
Author(s) Alicia Dickenstein, Federico N. Martinez, Laura Felicia Matusevich
TypeArticle in Journal
AbstractWe 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.
KeywordsA-hypergeometric functions, irregular holonomic D-modules, formal Nilsson series, Gröbner degenerations in the Weyl algebra
ISSN0213-2230; 2235-0616/e
URL http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=28&iss=3&rank=3
JournalRev. Mat. Iberoam.
PublisherEuropean Mathematical Society (EMS) Publishing House, Zurich
Translation No
Refereed No