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, the book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. The book describes many significant results and research directions developed by the author and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book would be useful for graduate students and researchers in complex analysis.
Preface The Nevanlinna theory The singular directions The deficient value theory The asymptotic value theory The relationship between deficient values and asymptotic values of an entire function The relationship between deficient values of a meromorphic function and direct transcendental singularities of its inverse functions Some supplementary results References.