代数体函数及其导数的公共Borel半径
Common Borel radius of an algebroid function and its derivative
摘要：
本文通过比较特征函数，证明了对于定义在单位圆盘上的任意$ν$值代数体函数$w(z)$，若其具有$\limsup_{r\to1-}T(r,w)/\log\frac{1}{1-r}=\infty$和超序$ρ_2(w)=0$，则$w(z)$和$w'(z)$的Borel半径分布相同.这是G.关于$\widehat{\mathbb{C}}$中亚纯函数的Valiron猜想.
英文摘要：
In this article, by comparing the characteristic functions, we prove that for any $ν$-valued algebroid function $w(z)$ defined in the unit disk with $\limsup_{r\to1-}T(r,w)/\log\frac{1}{1-r}=\infty$ and the hyper order $ρ_2(w)=0$, the distribution of the Borel radius of $w(z)$ and $w'(z)$ is the same. This is the extension of G. Valiron's conjecture for the meromorphic functions defined in $\widehat{\mathbb{C}}$.
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