Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
DARBOUX EVALUATIONS OF ALGEBRAIC GAUSS HYPERGEOMETRIC FUNCTIONS
Raimundas VIDUNAS
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ジャーナル フリー

2013 年 67 巻 2 号 p. 249-280

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Algebraic Gauss hypergeometric functions can be expressed explicitly in several ways. One attractive way is to pull-back their hypergeometric equations (with a finite monodromy) to Fuchsian equations with a finite cyclic monodromy, and express the algebraic solutions as radical functions on the covering curve. This article presents these pull-back transformations of minimal degree for the hypergeometric equations with the tetrahedral, octahedral or icosahedral projective monodromy. The minimal degree is 4, 6 or 12, respectively. The covering curves are called Darboux curves, and they have genus zero or (for some icosahedral Schwarz types) genus one.
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© 2013 Faculty of Mathematics, Kyushu University
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