On the existence of T -direction of algebroid functions: A problem of J.H. Zheng ✩

In this paper, we solve a problem of J.H. Zheng (see Problem 5.12 of [J.H. Zheng, On value distribution ofmeromorphic functions with respect to arguments, preprint]) by proving that for any ν-valued algebroid function satisfying lim supr→∞ T (r,w) log2 r =+∞, there exists a T -direction dealing with multiple values of w(z). © 2007 Elsevier Inc. All rights reserved.