一类复合整函数的亏量的进一步性质(英文)

Further Properties on the Deficiencies of a Class of Composite Entire Functions

设f和g是两个超越整函数,且T(r,f)=O ((logr)νe(logr)α),T(r,g)=O ((logr)β)(即存在4个正常数K1,K2和K3,K4,使有K1T(r,f)(logr)νe(logr)α K2和K2 T(r,g)(logr)β K4).其中ν>0,0<α<1,β>1和αβ<1.则对任何a≠∞,有δ(a,f(g))=δ(a,f),这个结果改进了Goldstein的结果.

Let f and g are two transcendental entire function with T(r,f)=O*((log r)νe(log r)α ))and T(r,g)=O*((log r)β)(i.e.,there exists four positive constants K1,K2 and K3,K4 such that K1T(r,f)(log r)νe(log r)α K2 and K3T(r,g)(log r)βK4). where ν>0,0<α<1,β>1 and αβ<1. Then δ(a,f(g))=δ(a,f). for any value of a≠∞.Those result improves the result of Goldstein.