Meromorphic functions of bounded valence on an open Riemann surface

Value-sharing of meromorphic functions on a Riemann surface

We present some results on two meromorphic functions from S to Ĉ sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus, the complex plane. Mathematics Subject Classification (2000): 30D35, 30F10

Meromorphic Functions on Certain Riemann Surfaces

1. Throughout the paper we shall denote by R a Riemann surface. For a domain Í2 in P, we represent by AB(Q) the class of all the singlevalued bounded analytic functions on the closure Ü. For a meromorphic function / on a domain ß, we use the notation viw\f, Q.) to express the number of times that/ attains w in ß. Definition 1. We say that REWIb if the maximum principle suplen \fip)\ =sup3,ean \...

Valuations on Meromorphic Functions of Bounded Type

The primary purpose of this paper is to show that every valuation on the field of meromorphic functions of bounded type on a finitely sheeted unlimited covering Riemann surface is a point valuation if and only if the same is true on its base Riemann surface. The result is then applied to concrete examples and some related results are obtained. Any valuation on the field M(W) of single valued me...

On Meromorphic Functions of Bounded Characteristic

Some Unsolved Problems on Meromorphic Functions of Uniformly Bounded Characteristic

The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the fsmily of holomorr.hc f11nctonz of bounded mesn oscilltion in R. After a survey some open problems are proposed in contrast with BMOA(R).