Abstract
In this article, by comparing the characteristic functions, we prove that for any ν-valued algebroid function w(z) defined in the open unit disk with \({\limsup_{r\rightarrow1-}T(r,w)/\log\frac{1}{1-r}=\infty}\) and the hyper order ρ 2(w) = 0, the distribution of the Borel radii 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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Wu, N., Xuan, Zx. Common Borel Radii of an Algebroid Function and Its Derivative. Results. Math. 62, 89–101 (2012). https://doi.org/10.1007/s00025-011-0132-y
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DOI: https://doi.org/10.1007/s00025-011-0132-y