[1] Qiu Huiling,. On meromorphic functions sharing one value [J]. Journal of Southeast University (English Edition), 2003, 19 (2): 200-204. [doi:10.3969/j.issn.1003-7985.2003.02.022]

Copy

On meromorphic functions sharing one value()

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 2

Page:

200-204

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-06-30

Info

Title:

On meromorphic functions sharing one value

Author(s):

Qiu Huiling

Department of Mathematics, Jiangsu Institute of Education, Nanjing 210013, China
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China

Keywords:

meromorphic function;  sharing value;  deficiency

PACS:

O174.5

DOI:

10.3969/j.issn.1003-7985.2003.02.022

Abstract:

The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0, f)+δ(0, g)+δ(∞, f)+δ(∞, g)=3 or δ₂(0, f)+δ₂(0, g)+δ₂(∞, f)+δ₂(∞, g)=3, and E(1, f)=E(1, g) then f(z), g(z) must be one of five cases.

References:

[1] Hayman W K. Meromorphic functions[M]. Clarendon: Oxford University Press, 1964.1-20
[2] Yang L. Value distribution theory[M]. Berlin: Spring-Verlag, 1993.
[3] Li P, Yang C C. Some further results on the unique range sets of meromorphic functions[J]. Kodai Math J, 1995, 18: 437-450.
[4] Yang C C. On deficiencies of differential polynomials[J]. Math Z, 1972, 125: 107-112.
[5] Yi H X. Meromorphic functions with two deficient values[J]. Acta Math, 1987, 30: 588-597.(in Chinese)
[6] Xu W S, Fang M L. On a theorem of Ozawa[J]. Math Study, 1996, 29:25-28.
[7] Nevanlinna R. Einige eindeutigkeitssätze in der theorie der meromorphen funktionen[J]. Acta Math, 1926, 48: 367-391.

Memo

Memo:

Biography: Qiu Huiling(1957—), female, associate professor, qiuhuiling1304@sina.com.

Common functions