|Table of Contents|

Picard Exceptional Sets for Meromorphic Functions(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2011年04期
Page:
26-32
Research Field:
数学
Publishing date:

Info

Title:
Picard Exceptional Sets for Meromorphic Functions
Author(s):
Wang Pinling; Wang Liqing
School of Mathematics and Information,Shanghai Lixin University of Commerce,Shanghai 201620,China
Keywords:
entire function; meromorphic function; Picard set; ε set
PACS:
O174.52
DOI:
-
Abstract:
In this paper we prove that if f( z) is a transcendental meromorphic function satisfying δ( ∞，f) ＞ 0，and n，k are positive integers satisfying n≥k + 2，then there exists a sequence of small disks whose centers tend to infinity such that ( fn ) ( k) takes each finite nonzero complex value infinitely times outside these disks．

References:

［1］ 杨乐． 值分布论及其新研究［M］． 北京: 科学出版社，1982．
［2］ Hayman W K． Picard values of mermorphic function and their derivatives［J］． Ann of math，1959， 70( 2) : 9-42．
［3］ Clunie J． On a result of hayman［J］． J London Math Soc，1967，42: 389-392．
［4］ Anderson J M，Baker I N，Clunie J G． The distribution of values of certain entire and meromorphic function［J］． Math Z， 1981，178: 509-525．
［5］ Langley J K． Analogues of Picard set for entire function and their derivatives［J］． Contemporary Math，1983，25: 75-86．
［6］ Chen H H． Yoshida functions and Picard values of integral functions and their derivatives［J］． Bull Austral Math Soc，1996， 54: 373-381．
［7］ 王品玲． 整函数导数的Picard 例外集［J］． 数学学报，2009，52( 5) : 961-968．
［8］ Wang Y F，Fang M L． Picard values and normal families of mermorphic functions with multiple zeros［J］． Acta Mathematica Sinica，1998，14( 1) : 17-26．
［9］ 詹小平，蔡海涛． 亚纯函数的例外集［J］． 数学学报，2001，44( 4) : 657-666．
［10］ Ahlfors L V． Complex Analysis［M］． New York: McGraw-Hill Book Company，1966．

Memo

Memo:
-
Last Update: 2013-03-21