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[1] Qiu Huiling**,. On a Result of Niino and Ozawa* [J]. Journal of Southeast University (English Edition), 2001, 17 (2): 84-86. [doi:10.3969/j.issn.1003-7985.2001.02.021]
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On a Result of Niino and Ozawa*()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
17
Issue:
2001 2
Page:
84-86
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2001-12-30

Info

Title:
On a Result of Niino and Ozawa*
Author(s):
Qiu Huiling**
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China
Department of Mathematics, Jiangsu Education College, Nanjing 210013, China
Keywords:
entire function;  meromorphic function;  deficiency
PACS:
O174.5
DOI:
10.3969/j.issn.1003-7985.2001.02.021
Abstract:
In this paper, we study the deficient relation of some transcendental entire functions. If fj(z)(j=1, 2, …, p) be transcendental entire functions, and let aj(j=1, 2, …, p) be nonzero finite complex numbers. If ∑pj=1ajfj(z)≡1, then ∑pj=1δp-1(0, fj)≤p-1, where δp-1(0, fj)=1-lim-r→∞(Np-1(r, 1/fj))/(T(r, fj))(j=1, 2, …, p). The result improves a result of Niino and Ozawa. Meanwhile we give some applications of our result.

References:

[1] W.K.Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964
[2] L.Yang, Value distribution theory, Springer-Verlag, Berlin, 1993
[3] K.Niino, and M.Ozawa, Deficiencies of an entire algebroid function, Kodai Math. Sem. Rep., vol.22, pp.98-113, 1970
[4] H.X.Yi, and C.C.Yang, Unicity theory of meromorphic functions(In Chinese), Science Press, Beijing, 1995
[5] W.K.Hayman, Waring’s problem für analytische Funktionen, Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber, pp.1-13, 1985
[6] G.G.Gundersen, Meromorphic solutions of f6+g6+h6≡6661, Analysis, vol.18, pp.285-290, 1998
[7] M.L.Fang, and X.H.Hua, Entire functions that share one small function, J. of Nanjing Univ. Mathematical Biquarterly, vol.17, no.2, pp.167-172, 2000

Memo

Memo:
* The project supported by the National Natural Science Foundation of China(10071038)and the National Science Foundation of Educational Department of Jiangsu Province(OOKJB110004).
** Born in 1957, female, associate professor.
Last Update: 2001-06-20