Theory of Entire and Meromorphic Functions: Deficient and Asymptotic Values and Singular Directions

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American Mathematical Soc., Jan 1, 1993 - Mathematics - 375 pages
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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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Contents

The Singular Directions
37
The Deficient Value Theory
109
The Asymptotic Value Theory
195
The Relationship between Deficient Values and Asymptotic
271
The Relationship between Deficient Values of
349
Some Supplementary Results
369
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Page 1 - We denote ...... (n(r,f), a = oc, n(r,a) = n(r,f = a) = \ (n(r,jÚ┐), a^oo as the number of roots of the equation f(z) = a in the disk |z| < r...

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