关于亚纯代数体函数的奇异方向

On Singular Directions of Meromorphic Algebroidal Functions

设T(r,w)满足:则一定存在一条方向使对任意给定N>0,任意复数a(至多有2u个例外值),有设T(r,w)满足:则一定存在一条方向对任意复数a(至多有2v个例外值),有(σ=M-2或σ=M-2-ε).即使在亚纯函数,这些奇异方向也未见研究.

Let w（z） be a meromorphic algebroidal function for ｜z｜〈＋∞. If limr →∞lg T（r, w）/lg r =0, limr →∞lg T（r, w）/lg lg r =＋∞, then there exists a direction arg z=θ0 such that, for any N〉0, ∑i1/（lg｜zi（a; △（θ0, δ））｜）N=＋∞, with 2 v possible exceptions for a. If limr →∞T（r, w）/lgKr =＋∞, limr →∞lg T（r, w）/lg lg r =M, then there exists a direction arg z=θ0 such that ∑i 1/lg｜zi（a; △（θ0, δ））｜）σ=∞ （σ=M-2 or σ=M-2-ε）, with 2 v possible exceptions for a. For meromorphic functions, these singular directions have not been studied yet.