关于亚纯代数体函数奇异方向的存在性

本文证明了如下结果:对于有穷正级亚纯代数体函数,一定存在一条奇异方向L∶arg z=θ0(0≤θ0＜2π),使得对于任意δ∈(0,π/2),在角域Δ(θ0,δ)内,对任意复数a,对任意ε＞0,有∑i1|zi(a;Δ(θ0,δ))|σ=∞(σ等于ρ或ρ-ε)至多有2v个例外a值.

On Existence of Singular Directions for Meromorphic Algebroidal Functions

Let w(z) be a meromorphic algebriodal function of finite order ρ > 0 for | z |<∞. Then there exists a direction L : arg z = θ_0 , which satisfies Σ_i1/|z_i(a;Δ(θ_0,δ))|~σ=∞(σ = ρ or σ =ρ-ε) for any ε>0,δ ∈ (0,π/2) , with 2v possible exceptions for a.