ON HYPERELLIPTIC SCHOTTKY GROUPS

A compact Riemann surface of genus g is hyperelliptic if it is a two sheeted covering of the Riemann sphere branched at 2(g*1) points; that is, if it satisfies a polynomial equation of the form: wz: (z as)(z ar) (z ar)... (, orn *r), whete ao, k:0,...,2g11 are distinct points on the Riemann sphere. There are various characterizations of hyperelliptic surfaces in the literature but none of them involve uniformization theory. In uniformization theory we begin with a surface a covering space § and the corresponding group of cover transformations G. If we can realize § as a plane domain Q, and G as a group of linear fractional transforma-tion.s i-, such that the projection map n: Q Qlf: S is holomorphic, then.l- is sai