Theory of Entire and Meromorphic Functions: Deficient and Asymptotic Values and Singular Directions
This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.
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The Singular Directions
The Deficient Value Theory
The Asymptotic Value Theory
The Relationship between Deficient Values and Asymptotic
The Relationship between Deficient Values of
Some Supplementary Results
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6k+l according to formula according to Lemma according to Theorem Analogously analytic curve annulus applying Lemma applying Theorem assume asymptotic path Borel direction boundary circumference conclude connected component consider the transformation constant independent containing point continuous curve Corollary corresponding denote direct transcendental singularities direction of f(z domain entire function exists a point exists value finite asymptotic values finite complex number finite deficient values Furthermore Hence intersection point interval inverse function Julia directions Let f(z level curve linear measure log+ log2 lower order Math maximum modulus principle meas meromorphic function Moreover Nevanlinna Nevanlinna Theory Notice number h obtain open plane point z point z0 positive integer proof of Theorem prove the following proved completely pseudo-non-Euclidean r—+oc logr Rm+l satisfying formula sequence rn simply connected spherical distances sufficiently large Suppose tending to oc Theorem 3.l unit disk values of f(z z-plane