零级代数体函数的最大型Borel方向

On the Borel Directions of Largest Type for an Algebroid Function of Zero Order

证明了当ν值零级代数体函数w(z)满足条件limr→∞T(r ,w)(logr) 2 =∞时至少存在一条最大型Borel方向argz =θ0 ,满足 0 <limr→∞n(r ,Δ(θ0 ) ,a)(logr) λ(r) -1≤eνλ ,至多除去两个例外值a。得出几个关于n(r ,Δ(θ ,ε) ,a)的级和型的推论。

It is proved that when a ν value algebroid function w(z) satisfies the condition lim r→∞T(r,w) (log r) 2=∞ , there at least exists a Borel direction of the largest type arg z=θ 0 , satisfying 0< lim r→∞n(r,Δ(θ 0),a) (log r) λ(r)-1 ≤e νλ , at most with two exceptional values a. Further, two corollaries about the order and the type of n(r,Δ(θ,ε),a) are obtained.