an:05231227
Zbl 1170.30011
Bhoosnurmath, Subhas S.; Dyavanal, Renukadevi S.
Uniqueness and value-sharing of meromorphic functions
EN
Comput. Math. Appl. 53, No. 8, 1191-1205 (2007).
00208764
2007
j
30D35
meromorphic function; entire function; shared values; differential polynomial; uniqueness
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 \(f\equiv g\).
Dov Aharonov (Haifa)