代数体函数在Borel方向上a值点个数的型

THE TYPE OF THE a--VALUEPOINTS OF AN ALGEBROID FUNCTION IN A BOREL DIRECTION

本文证明了若υ值代数体函数w(z)有有穷正级λ(或有穷对数级ρ,ρ≥2)。其型μ(或对数型σ,ρ=2时σ=∞)为∞,或有穷正数,或零。则至少在一条Borel方向上的任意角域内α值点个数的型(或对数型)也同时为∞,或有穷正数,或零。至多除去2υ个例外的复数α。

In this paper the author has proved that if the order λ of a v-value algebroid function isfinite positive(or logarithmic order ρ is finite,ρ≥2), and its type μ (or logarithmic type σ,if ρ=2 then σ=∞) is infinity, or finite positive,or zero,there is at least a Borel direction,in which any angular domain the type of the number of the a-value points is infinity, orfinite positive, or zero too, at most there is 2υ exceptional value α