Common Borel radius of an algebroid function and its derivative

Details Common Borel radius of an algebroid function and its derivative Common Borel radius of an algebroid function and its derivative

2009-06-24

arxiv.org/abs/0906.4409v1

Mathematics

Complex Variables

Scientific paper

In this article, by comparing the characteristic functions, we prove that for any $\nu$-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 $\rho_2(w)=0$, 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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