Algebroid functions with given Borel points

作者:Wu, Zhao-Jun*; Zhang, Shao-Hua
来源:Georgian Mathematical Journal, 2015, 22(2): 289-294.
DOI:10.1515/gmj-2015-0018

摘要

In this paper, we prove the following result. Suppose that E is an arbitrary non-empty closed set of real numbers (mod 2 pi). Then for any positive lambda (0 < lambda < infinity), there exists an algebroid not meromorphic) w (z) of order lambda in the unit disc, such that every point e(i theta), theta is an element of E, on the unit circle is a Borel point of order lambda of w (z) and w (z) has no other Borel point of order lambda. This result generalizes the related results of a meromorphic function due to Lo Yang, Guanghou Zhang, Daochun Sun and Zongsheng Gao.

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