MR2440943 Ryoichi KOBAYASHI, Tatsuya NISHIZAKA, Shoji SHINZATO and Masaaki YOSHIDA Ryoichi KOBAYASHI, Tatsuya NISHIZAKA, Shoji SHINZATO and Masaaki YOSHIDA Funkcialaj Ekvacioj. Serio Internacia 51 2008 281--305 http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-2/51_281.pdf http://www.ams.org/mathscinet-getitem?mr=MR2440943 We propose an affine version of the Schwarz map for the hypergeometric differential equation, and study its image when the monodromy group is finite. Hypergeometric differential equation, Schwarz map, Invariants of polyhedral groups. 33C05, 53C42. 51-281 2008 Ryoichi KOBAYASHI, Tatsuya NISHIZAKA, Shoji SHINZATO and Masaaki YOSHIDA Ryoichi KOBAYASHI, Tatsuya NISHIZAKA, Shoji SHINZATO and Masaaki YOSHIDA 1 Iwasaki, K.; Kimura, H.; Shimomura, S.; Yoshida, M. From Gauss to Painlevé -- A modern theory of special functions Vieweg Verlag, Wiesbaden 1991 MR1118604 2 Koike, M., Modular forms on non-compact arithmetic triangle groups, preprint (2005) 3 Kobayashi, R., Affine Schwarz map for the hypergeometric equation (in Japanese), Master thesis Kyushu Univ. (2007) (http://www.math.kyushu-u.ac.jp/~myoshida/RKobayashi.pdf)

4 Nishino, T. J. Math. Kyoto Univ. 8 1968 49--100 MR0235157