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arXiv · 0906.4409

Common Borel radius of an algebroid function and its derivative

Nan Wu·Zuxing Xuan
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Abstract

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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Nan Wu, Zuxing Xuan. 2009-06-24. Common Borel radius of an algebroid function and its derivative. https://arxiv.org/abs/0906.4409

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