A system of hypergeometric differential equations in two variables of rank 9

2016/08/09 by Jyoichi Kaneko, Kaneko, Jyoichi, Keiji Matsumoto +3 · 1 citation
Mathematics · Physics and Astronomy · #32S40 #33C70 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:32S40 #msc:33C70

paper · pdf · doi:10.48550/arxiv.1608.02667

35 pages, 4 figures

openalex publication_date 2016/08/09 · arxiv created 2016/08/23 · arxiv updated 2016/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank 9. We give a fundamental system of solutions to this system in terms of this hypergeometric series. We give circuit matrices along generators of the fundamental group of the complement of its singular locus with respect to our fundamental system.

Citations

• Monodromy representations of hypergeometric systems with respect to fundamental series solutions

Cited by

• The monodromy representation of a hypergeometric system in m variables of rank p^m

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