open access

https://hdl.handle.net/2115/90608

Logarithmic A-hypergeometric series II

英語

The method of Frobenius

2022

Springer

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

64(4)

1057-1086

In this paper, following (Saito in Int J Math 31(13):2050110, 2020), we continue to develop the perturbingmethod 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 perturbingmethod. In addition, we give a sufficient condition for a given fake exponent to be an exponent. As important examples of themain results, we give fundamental systems of series solutions to Aomoto-Gel'fand systems and to Lauricella's F-C systems with special parameter vectors, respectively.

学術雑誌論文

Accepted Manuscript

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s13366-022-00669-5

0138-4821