On fixed-points and singular values of transcendental meromorphic functions  

作　　者：ZHENG JianHua Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 

出　　处：《Science China Mathematics》2010年第3期887-894,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871108)

摘　　要：In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for hyperbolic domains.In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for hyperbolic domains.

关 键 词：MEROMORPHIC functions fixed POINTS SINGULAR POINTS HYPERBOLIC metric COVERING mapping 

分 类 号：O174.52[理学—数学]