Uniqueness and value-sharing of meromorphic functions. (English) Zbl 1170.30011

Using Nevanlinna theory, the authors improve some earlier results concerning value-sharing of meromorphic functions. The authors recall related theorems of Chume-Hayman and Zang-Hua. Hennekemeter, Chen, and Wang gave (independently) some extensions of the above quoted theorems. Fang further extended these theorems, where uniqueness statements are in the center of discussion. Here the authors give further natural generalizations and similar theorems. We mention their theorem 4: Let \(f(z)\) and \(g(z)\) be two non-constant meromorphic functions satisfying a certain condition which we don’t quote. Then if \([f^n (f-1)]^{(k)}\) and \([g^n(g-1)]^{(k)}\) share \(1\) CM, it follows that \(f\equiv g\).


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI


[1] Hayman, W.K., Meromorphic functions, (1964), Clarendon Press Oxford · Zbl 0115.06203
[2] Yang, L., Value distribution theory, (1993), Springer-Verlag Berlin
[3] Hayman, W.K., Picard values of meromorphic functions and their derivatives, Ann. of math., 70, 9-42, (1959) · Zbl 0088.28505
[4] Clunie, J., On a result of Hayman, J. London math. soc., 42, 389-392, (1967) · Zbl 0169.40801
[5] Fang, M.L.; Hua, X.H., Entire functions that share one value, J. Nanjing univ. math. biquarterely, 13, 1, 44-48, (1996) · Zbl 0899.30022
[6] Yang, C.C.; Hua, X.H., Uniqueness and value-sharing of meromorphic functions, Ann. acad. sci. fenn. math., 22, 2, 395-406, (1997) · Zbl 0890.30019
[7] Fang, M.L., Uniqueness and value-sharing of entire functions, Comput. math. appl., 44, 823-831, (2002) · Zbl 1035.30017
[8] Fang, M.L.; Hong, W., A unicity theorem for entire functions concerning differential polynomials, Indian J. pure appl. math., 32, 9, 1343-1348, (2001) · Zbl 1005.30023
[9] Lin, W.-C.; Yi, H.-X., Uniqueness theorems for meromorphic function, Indian J. pure appl. math., 32, 9, 121-132, (2004) · Zbl 1056.30031
[10] Hennekemper, G.; Hennekemper, W., Picard ausnahmewerte von ableitungen gewisser meromorpher funktionen, Complex var., 5, 87-93, (1985) · Zbl 0537.30017
[11] Chen, H.H., Yoshida functions and Picard values of integral function and their derivatives, Bull. austral. math. soc., 54, 373-381, (1996) · Zbl 0879.30018
[12] Wang, Y.F., On mues conjecture and Picard values, Sci. China, 36, 1, 28-35, (1993) · Zbl 0777.30017
[13] Wang, Y.F.; Fang, M.L, Picard values and normal families of meromorphic functions with multiple zeros, Acta math. sinica (N.S.), 14, 1, 17-26, (1998) · Zbl 0909.30025
[14] Frank, G., Eine vermutung von Hayman uber nullstellen meromorpher funktion, Math. Z., 149, 29-36, (1976) · Zbl 0312.30032
[15] Yi, H.X.; Yang, C.C., Unicity theory of meromorphic functions, (1995), Science Press Beijing
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.