Painlev\'e-Umemura extensions

MR1285481 Nishioka, K. K. NISHIOKA Painlev\'e-Umemura extensions Funkcialaj Ekvacioj. Serio Internacia 37 1994 59--64 http://fe.math.kobe-u.ac.jp/FE/Free/vol37/fe37-1-4.pdf http://fe.math.kobe-u.ac.jp/FE/FE_pdf_with_bookmark/FE35-40-en_KML/fe37-059-064/fe37-059-064.pdf http://www.ams.org/mathscinet-getitem?mr=MR1285481 fe37-059-064 1994 Painlevé-Umemura Extensions NISHIOKA, K. NISHIOKA, K. 1 Buium, A. Differential function fields and moduli of algebraic varieties Lecture Notes in Math 1226 Lecture Notes in Math., 1226, Springer, Berlin 1986 MR0874111 100 Cache/Bu/Buium,*,*,1986,1987 x+146 2 Kolchin, E. R. Differential algebra and algebraic groups Academic Press, New York 1973 MR0568864 100 Cache/Ko/Kolchin,*,*,1973,1974 xviii+446 3 Matsuda, M. First order algebraic differential equations Lecture Notes in Math 804 Lecture Notes in Math., 804, Springer, Berlin 1980 MR0576060 75 Cache/Ma/Matsuda,algebraic,*,1980,1981 vi+111

4 Nishioka, K. A class of transcendental functions containing elementary and elliptic ones Osaka J. Math. 22 1985 743-753 MR0815443 100 Cache/Ni/Nishioka,transcendental,Osaka*,1985,1986

5 Nishioka, K. A note on the transcendency of Panilevé's first transcendent Nagoya Math. J. 109 1988 63-67 MR0931951 88 Cache/Ni/Nishioka,transcendency,Nagoya*,1988,1989

6 Nishioka, K. General solutions depending algebraically on arbitrary constants Nagoya Math. J. 113 1989 1-6 MR0986432 100 Cache/Ni/Nishioka,algebraically,Nagoya*,1989,1990

7 Nishioka, K. Differential algebraic function fields depending rationally on arbitrary constants Nagoya Math. J. 113 1989 173-179 MR0986443 100 Cache/Ni/Nishioka,*,Nagoya*,1989,1990

8 Painlevé, P. Leçons de Stockholm, Œuvres de P. Painlevé I Éditions du C.N.R.S., Paris 1973 MR0532682

9 Umemura, H. On the irreducibility of the first differential equation of Painlevé Algebraic Geometry and Commutative Algebra in honor of Masayosi NAGATA, Kinokuniya, Tokyo 1987 771-789 MR0977782 85 S\=ugaku Cache/Um/Umemura,irreducibility,*,1987,1988

10 Umemura, H. Second proof of the irreducibility of the first differential equation of Painlevé Nagoya Math. J. 117 1990 125-171 MR1044939 100 Cache/Um/Umemura,irreducibility,Nagoya*,1990,1991

11 Umemura, H. Birational automorphism groups and differential equations Nagoya Math. J. 119 1990 1-80 MR1071899 100 Cache/Um/Umemura,automorphism,Nagoya*,1990,1991