具有亏函数的整函数与亚纯函数的复合增长性(英文)

Growth of Composite for Entire Functions and Meromorphic Functions with Deficient Functions

设f是超越整函数,且T(r, f) = O((logr)βexp((logr)α))(0<α<1,β>0) ,即存在两个正实数K1和K2,使得K1≤(logr)Tβe(xrp,( (fl)ogr)α)≤ K2设g1和g2是超越整函数, g2的级是ρg2(0<ρg2<∞) ,又设ai(z) (i =1,2,…,n, n≤∞)是整函数,且满足T(r, ai(z))=o( T(r, g2))及∑ni =1δ(ai(z) , g2) =1和δ(ai(z) , g2) >0.如果T(r, g1) =o( T(r, g2)) (r→∞)则T(r, f(g1)) =o( T(r, f(g2)))

In this paper, the following results are obtained： Let f be a transcendental meromorphic functions with T（r,f）=O（（log r）^β exp（（log r）^α）） 0〈α〈1,β〉0 i. e. , there exists two positive constants K1 and K2 such that K1≤T（r,f）/（log r）^β exp（（log r）^α）≤K2;let g1 and g2 are transcendental entire functions and the order of g2 be ρg2 （0 〈 ρg2 〈 ∞）, let ai（z） （i = 1,2,...,n, n ≤∞） be entire functions which satisfying T（r, ai （z） ） = o（T（r, g2 ） ） with ∑i-1nδ（ai（z）,g2）=1 δ（ai（z）,g2）〉0 If T（r, g1） = o（T（r, g2）） （r→∞）, then T（r,f（g1））=o（T（r,f（g2））） r→∞