Value Distribution Theory

Authors: Lo, Yang

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About this book

It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep­ tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 < A < (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-662-02915-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA in USD
  • ISBN 978-3-662-02917-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Value Distribution Theory
Authors
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
Distribution Rights
Distribution rights for The People's Republic of China: Science Press, Beijing
eBook ISBN
978-3-662-02915-2
DOI
10.1007/978-3-662-02915-2
Softcover ISBN
978-3-662-02917-6
Edition Number
1
Number of Pages
XII, 269
Number of Illustrations
2 b/w illustrations
Additional Information
Jointly published with Science Press, Beijing. Original Chinese edition published by Science Press, Beijing 1982
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