Translations of Mathematical Monographs
2008;
488 pp;
Hardcover
MSC: Primary 30;
Print ISBN: 978-0-8218-4265-2
Product Code: MMONO/236
List Price: $133.00
AMS Member Price: $106.40
MAA Member Price: $119.70
Electronic ISBN: 978-1-4704-4657-4
Product Code: MMONO/236.E
List Price: $133.00
AMS Member Price: $106.40
MAA Member Price: $119.70
Supplemental Materials
Value Distribution of Meromorphic Functions
Share this pageAnatoly A. Goldberg; Iossif V. Ostrovskii
This book contains a comprehensive exposition of the Nevanlinna theory
of meromorphic functions of one complex variable, with detailed study
of deficiencies, value distribution, and asymptotic properties of
meromorphic functions.
A self-contained exposition of the inverse problem for meromorphic
functions of finite order with finitely many deficiencies is given in
full detail. Many results included in the book belong to the authors,
and were previously available only in journal articles.
The main body of the book is a translation of the Russian original
published in 1970, which has been one of the most popular sources in
this field since then. New references and footnotes related to recent
achievements in the topics considered in the original edition have
been added and a few corrections made. A new Appendix with a survey of
the results obtained after 1970 and extensive bibliography has been
written by Alexandre Eremenko and James K. Langley for this English
edition.
The only prerequisite for understanding material of this book is an
undergraduate course in the theory of functions of one complex
variable.
Readership
Graduate students and research mathematicians interested in complex analysis.
Table of Contents
Table of Contents
Value Distribution of Meromorphic Functions
- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface xi12
- Preface to the Russian edition xiii14
- Characteristics of the behavior of a meromorphic function and the first fundamental theorem 118
- Meromorphic functions of finite order 4360
- The second fundamental theorem 87104
- Deficient values 113130
- Asymptotic properties of meromorphic functions and deficiencies 171188
- Value distribution with respect to the arguments 259276
- Applications of Riemann surfaces to value distribution 331348
- On the magnitude of type for an entire function 429446
- Notes 439456
- A survey of some results after 1970 453470
- Bibliography 467484
- References added to the English edition 475492
- Author index 481498
- Subject index 485502
- Notation index 487504
- Back Cover Back Cover1506