TY - JOUR
T1 - Uniqueness theorems of meromorphic functions of a certain form
AU - Xu, Junfeng
AU - Han, Qi
AU - Zhang, Jilong
PY - 2009
Y1 - 2009
N2 - In this paper, we shall show that for any entire function f, the function of the form fm(fn 1)f′ has no non-zero finite Picard value for all positive integers m, n ∈ N possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if fm(fn-1)f′ and gm(gn-1)g′ share the value 1 weakly, then f ≡ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.
AB - In this paper, we shall show that for any entire function f, the function of the form fm(fn 1)f′ has no non-zero finite Picard value for all positive integers m, n ∈ N possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if fm(fn-1)f′ and gm(gn-1)g′ share the value 1 weakly, then f ≡ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.
KW - Entire function
KW - Meromorphic function
KW - Picard value
UR - https://www.scopus.com/pages/publications/77749274573
U2 - 10.4134/BKMS.2009.46.6.1079
DO - 10.4134/BKMS.2009.46.6.1079
M3 - 文章
AN - SCOPUS:77749274573
SN - 1015-8634
VL - 46
SP - 1079
EP - 1089
JO - Bulletin of the Korean Mathematical Society
JF - Bulletin of the Korean Mathematical Society
IS - 6
ER -