Value Distribution Theory and New Research - Hardcover

Lo, Yang

Hardcover

ISBN 10: 3540543791 ISBN 13: 9783540543794

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1993

Synopsis

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 (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.

About this title

Synopsis

A summary of contemporary research being carried out in China on value distribution theory, this volume focuses on Borel directions and filling disks - topics that provide a new angle to the study of this subject. It assesses the value distribution theory of entire and meromorphic functions.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1993
• Language: English
• ISBN 10: 3540543791
• ISBN 13: 9783540543794
• Binding: Hardcover
• Number of pages: 269