## Tohoku Mathematical Journal 2003 June SECOND SERIES VOL. 55, NO. 2

 Tohoku Math. J. 55 (2003), 189-205

Title MONODROMY GROUPS OF HYPERGEOMETRIC FUNCTIONS SATISFYING ALGEBRAIC EQUATIONS

Author Mitsuo Kato and Masatoshi Noumi

(Received May 11, 2001, revised May 7, 2002)
Abstract. The solutions of the algebraic equation \$y^{mn}+x y^{mp}-1=0\$ with \$n>p\$ and \$m\geq 2\$ satisfy a generalized hypergeometric differential equation with imprimitive finite irreducible monodromy group. Thanks to this fact, we can determine the monodromy group and the Schwarz map of the differential equation.

2000 Mathematics Subject Classification. Primary 33C20.

Key words and phrases. Hypergeometric function, generalized binomial function, monodromy group.