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International Journal of Mathematics and Mathematical Sciences
Volume 8, Issue 3, Pages 477-482

Some unsolved problems on meromorphic functions of uniformly bounded characteristic

Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, Tokyo 158, Japan

Received 14 February 1985

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 family of holomorphic functions of bounded mean oscillation in R. After a survey some open problems are proposed in contrast with BMOA(R).