关于亚纯代数体函数的奇异方向

设T(r, w)满足:lim_{r →∞}lg T(r, w)/lg r =0,lim_r→∞lg T(r, w)/lg lg r =+ ∞, 则一定存在一条方向arg z=θ₀ ,使对任意给定N>0,任意复数 a (至多有2 v个例外值), 有∑_i1/(lg|z_i(a;?(θ₀,δ))|)^N=∞.设T(r, w)满足:lim_r→∞T(r, w)/lg^Kr =+∞,lim_r→+∞lg T(r, w) /lg lg r =M, 则一定存在一条方向argz=θ₀ ,对任意复数a (至多有2 v个例外值),有∑_i1/lg|z_i(a;?(θ₀,δ))|)^σ=∞(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.

On Singular Directions of |Meromorphic Algebroidal Functions

Let w(z) be a meromorphic algebroidal   function  for |z|<+∞. If lim_r →∞lg T(r, w)/lg r =0,  lim_r →∞lg T(r, w)/lg lg r =+∞, then there exists a direction arg z=θ₀ such that, for any N>0, ∑_i1/(lg|z_i(a; ?(θ₀, δ))|)^N=+∞, with 2 v possible exceptions for a. If lim_r →∞T(r, w)/lg^Kr =+∞,  lim_r →∞lg T(r, w)/lg lg r =M, then there exists a direction arg z=θ₀ such that ∑_i 1/lg|z_i(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.