Logarithmic A-hypergeometric series II

In this paper, following [6], we continue to develop the perturbing method of constructing logarithmic series solutions to a regular A-hypergeometric system. Fixing a fake exponent of an A-hypergeometric system, we consider some spaces of linear partial differential operators with constant coefficie...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Okuyama, Go, Saito, Mutsumi
Format: Article
Language:English
Subjects:
Differential equations
Operators (mathematics)
Online Access:Get full text
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Summary:In this paper, following [6], we continue to develop the perturbing method of constructing logarithmic series solutions to a regular A-hypergeometric system. Fixing a fake exponent of an A-hypergeometric system, we consider some spaces of linear partial differential operators with constant coefficients. Comparing these spaces, we construct a fundamental system of series solutions with the given exponent by the perturbing method. In addition, we give a sufficient condition for a given fake exponent to be an exponent. As important examples of the main results, we give fundamental systems of series solutions to Aomoto-Gel'fand systems and to Lauricella's FC systems with special parameter vectors, respectively.
ISSN:2331-8422