E-Book Overview
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.
Readership: Graduate students and researchers in complex analysis
E-Book Content
Translations of
MATHEMATICAL
MONOGRAPHS Volume 122
Theory of Entire and Meromorphic Functions Deficient and Asymptotic Values and Singular Directions Zhang Guan-Hou
American Mathematical Society
Translations of Mathematical Monographs
12 2
Theory of Entire and Meromorphic Functions Deficient and Asymptotic Values and Singular Directions
Translations of
MATHEMATICAL MONOGRAPHS Volume 122
Theory of Entire and Meromorphic Functions Deficient and Asymptotic Values and Singular Directions Zhang Guan-Hou
NN
9RUM4909it OL )1- 4 1*
Translated from the Chinese by Chung-Chun Yang 1991 Mathematics Subject Classification. Primary 30D30, 30D35. Library of Congress Cataloging-in-Publication Data
Zhang, Guan-Hou, 1937-1987. [Cheng han shu ho yeh ch'un han shu li lun. English] Theory of entire and meromorphic functions: deficient and asymptotic values and singular directions/Zhang Kuan-hua. p. cm.-(Translations of mathematical monographs; v. 122) ISBN 0-8218-4589-6 1. Functions, Entire. 2. Functions, Meromorphic. I. Title. II. Series. QA353.E5Z4313 1993 93-43 CIP 515'.98-dc2O
COPYING AND REPRINTING. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940-6248. The owner consents to copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that a fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, Massachusetts 01970. When paying this fee please use the code 0065-9282/93 to refer to this publication. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotion purposes, for creating new collective works, or for resale.
Copyright Q 1993 by the American Mathematical Society. All rights reserved. English translation published by the AMS, with the consent of Science Press. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. This publication was typeset using AMS-TEX, the American Mathematical Society's TEX macro system.
10987654321
989796959493
Contents
Preface
ix
Chapter 1. The Nevanlinna