Acta mathematica scientia, Series B >
CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE
Received date: 2014-04-20
Revised date: 2014-10-01
Online published: 2015-05-01
Supported by
The first author is supported by the National Natural Science Foundation of China (11201395). The second author is supported by the Science Foundation of Educational Commission of Hubei Province (D20132804). The third author is supported by the Science Foundation of Jiangxi Province (20122BAB201006).
In this article, some facts of the value distribution theory for meromorphic functions with maximal deficiency sum in the plane will be considered in the punctured plane, and also the relationship between the deficiency of meromorphic function in the punctured plane and that of their derivatives is studied.
Key words: Meromorphic function; maximal deficiency sum; punctured plane
Zhaojun WU , Sheng'an CHEN , Yuxian CHEN . CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE[J]. Acta mathematica scientia, Series B, 2015 , 35(3) : 673 -680 . DOI: 10.1016/S0252-9602(15)30012-6
[1] Cao T B, Deng Z S. On the uniqueness of meromorphic functions that share three or two finite sets on annuli. Proceedings Mathematical Sciences, 2012, 122(2): 203-220
[2] Cao T B, Yi H X. Uniqueness theorems of meromorphic functions shares sets IM on Annuli. Acta Math Sinica (Chin Ser), 2011, 54 (4): 623-632
[3] Cao T B, Yi H X, Xu H Y. On the multiple values and uniqueness of meromorphic functions on annuli. Comput Math Appl, 2009, 58(7): 1457-1465
[4] Chen Y X, Wu Z J. Exceptional values of meromorphic functions and of their derivatives on annuli. Ann Polon Math, 2012, 105: 154-165
[5] Edrei A. Sums of deficiencies of meromorphic functions II. J Analyse Math, 1967, 19: 53-74
[6] Fang M L. A note on a result of Singh and Kulkarni, Internat. J Math and Math Sci, 2000, 23: 285-288
[7] Fernández A. On the value distribution of meromorphic function in the punctured plane. Mathematychni Studii, 2010, 34: 136-144
[8] Goldberg A, Ostrovskii I. Value Distribution of Meromorphic Functions//Transl Math Monogr, Vol. 236. Providence, RI: American Mathematical Society, 2008; translated from the 1970 Russian original by Mikhail Ostrovskii, with an appendix by Alexandre Eremenko and James K. Langley
[9] Hayman W K. Meromorphic functions. Oxford: Oxford Mathematical Monographs Clarendon Press, 1964
[10] Khrystiyanyn A Ya, Kondratyuk A A. On the Nevanlinna Theory for meromorphic functions on annuli I. Mathematychni Studii, 2005, 23: 19-30
[11] Khrystiyanyn A Ya, Kondratyuk A A. On the Nevanlinna Theory for meromorphic functions on annuli II. Mathematychni Studii, 2005, 24: 57-68
[12] Kondratyuk A A, Laine I. Meromorphic functions in multiply connected domains//Fourier series methods in complex analysis (Mekrij¨arvi, 2005). Univ Juensuu Dept Ser, 2006, 10: 9-111
[13] Korhonen R. Nevanlinna Theory in an annulus. Value distribution theory and related topics//Adv Complex Anal and Applic. Kluwer Academic Publishers, 2004: 167-179
[14] Lahiri I. Milloux theorem and deficiency of vector-valued meromorphic functions. J Indian Math Soc, 1990, 55: 235-250
[15] Shan S M, Singh S K. On the derivative of a meromorphic function with maximum defect. Math Zeitschr, 1956, 65: 171-174
[16] Singh S K, Kulkarni V N. Characteristc function of a meromorphic function and its derivative. Ann Polon Math, 1973, 28: 123-133
[17] Weitsman Allen. Meromorphic functions with maximal deficiency sum and a conjecture of F. Nevanlinna. Acta Math, 1969, 123: 115-139
[18] Wu Z J, Chen Y X. Milloux inequality of meromorphic function in annuli. Journal of Mathematical Ineaualities, 2013, 7(4): 577-586
[19] Wu Z J. An inequality on the zeros and poles of vector valued meromorphic functions. Acta Mathematica Scientia, 2014, 34B(2): 380-386
[20] Yang L. Value distribution theory. Translated and revised from the 1982 Chinese original. Berlin: Springer- Verlag; Beijing: Science Press Beijing, 1993
/
| 〈 |
|
〉 |