Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 2: 355 - 376

DOI: https://doi.org/10.1007/s11464-014-0357-7

RESEARCH ARTICLE

Radically distributed value and normal families of meromorphic functions

  • Jianming QI 1,2 ,
  • Guowei ZHANG 3 ,
  • Wenjun YUAN , 2,4
Expand
  • 1. Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 200240, China
  • 2. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
  • 3. Department of Mathematics, Anyang Normal University, Anyang 455000, China
  • 4. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China

Received date: 26 Apr 2011

Accepted date: 16 Oct 2013

Published date: 01 Apr 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

We establish several upper-bound estimates for the growth of meromorphic functions with radially distributed value. We also obtain a normality criterion for a class of meromorphic functions, where any two of whose differential polynomials share a non-zero value. Our theorems improve some previous results.

Key words： Meromorphic function; Nevanlinna theory; normal family; angular characteristic function; radially distributed value

Cite this article

Jianming QI , Guowei ZHANG , Wenjun YUAN . Radically distributed value and normal families of meromorphic functions[J]. Frontiers of Mathematics in China, 2014 , 9(2) : 355 -376 . DOI: 10.1007/s11464-014-0357-7

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
BaernsteinA. Proof of Edrei’s spread conjecture. Proc Lond Math Soc, 1973, 26: 418-434

DOI

2
BergweilerW, EremenkoA. On the singularities of the inverse to a meromorphic function of finite order. Rev Mat Iberoam, 1995, 11(2): 355-373

DOI

3
ChenS J, LinW C, ChenJ F. on the growth of meromorphic functions with a radially distributed value. Indian J Pure Appl Math, 2011, 42(1): 53-70

DOI

4
ChuangC T. Sur la comparaison de la croissance d’une fonction méromorphe et de celle de sa dérivée. Bull Sci Math, 1951, 75: 171-190

5
EdreiA. Meromorphic functions with three radially distributed values. Trans Amer Math Soc, 1955, 78: 276-293 376 Jianming QI et al.

6
EdreiA. Sums of deficiencies of meromorphic function. J Analyse Math, 1965, 14: 79-107

DOI

7
FangM L, ZalcmanL. On value distribution of f + α(f′)n. Sci China Ser A, 2008, 38(3): 279-285

8
Gol’dbergA A, OstrovskiiI V. The Distribution of Values of Meromorphic Functions. Moscow: Izdat Nauka, 1970 (in Russian)

9
HaymanW K. Meromorphic Functions. Oxford: Clarendon Press, 1964

10
HaymanW K, MilesJ. On the growth of a meromorphic function and its derivatives. Complex Variables, 1989, 12: 245-260

DOI

11
HeY Z, XiaoX Z. Algebroid Functions and Ordinary Differential Equations. Beijing: Science Press, 1988 (in Chinese)

12
LaineI. Nevanlinna Theory and Complex Differential Equations. Berlin: de Gruyter, 1993

13
NevanlinnaR. Uber die eigenschaften meromorphic funktionen in einem winkelraum. Acta Soc Sci Feen, 1925, 50: 1-45

14
PangX C, ZalcmanL. Normal families and shared values. Bull Lond Math Soc, 2000, 32: 325-331

DOI

15
QiJ M, ZhuT Y. Some normal criteria about shared values with their multiplicity zeros. Abstr Appl Anal, 2010,

DOI

16
XuY, WuF Q, LiaoL W. Picard values and normal families of meromorphic functions. Proc Roy Soc Edinburgh Sect A, 2009, 139: 1091-1099

DOI

17
YangL. Borel directions of meromorphic functions in an angular domain. Sci China, 1979, (Math Ser I): 149-163

18
YangL, YangC C. Angular distribution of values of f f′. Sci China Ser A-Math, 1994, 37: 284-294

19
ZalcmanL. A heuristic principle in complex function theory. Amer Math Monthly, 1975, 82: 813-817

DOI

20
ZhengJ H. On transcendental meromorphic functions with radially distributed values. Sci China Ser A-Math, 2004, 47: 401-416

DOI

21
ZhengJ H. Value Distribution of Meromorphic Functions. Berlin: Springer, 2010

Options
Outlines

/

〈 〉