MINIMAL SCHWARZ MAPS OF ₃<i>F</i>₂ WITH FINITE IRREDUCIBLE MONODROMY GROUPS

• KATO Mitsuo

  Department of Mathematics College of Education University of the Ryukyus

抄録

The generalized hypergeometric function ₃F₂ (a₀, a₁, a₂; b₁, b₂; z) satisfies the Fuchsian differential equation ₃E₂ of rank three. Beukers and Heckman classified all of the possible parameter sets of ₃E₂ with finite irreducible primitive monodromy groups into 11 classes. In each of these classes, we determine the parameter set of ₃E₂ such that the image curve (in the projective plane) of the Schwarz map defined by the ratio of its three independent solutions attains the minimal degree.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 60 (1), 27-46, 2006

  九州大学大学院数理学研究院

キーワード

• hypergeometric function
• Schwarz map
• monodromy group
• plane curve

詳細情報

• CRID: 1390282680206716160
• NII論文ID: 130000063154
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.60.27
• ISSN: 18832032
• ISSN: 13406116
• MRID: 2216947
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/60/1/60_1_27/_pdf
• 本文言語コード: en
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