Common Borel Radii of an Algebroid Function and Its Derivative

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 ρ2(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 \({\widehat{\mathbb{C}}}\).