An algebroidal function of infinite order with given T directions
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摘要: 主要研究了具有给定T方向的无穷级亚纯函数与代数体函数的存在性问题. 利用循环赋值方式, 构造了一个无穷级代数体函数
$ \omega(z) $ , 使得对任意给定的非空闭实数集$ E\pmod {2\pi} $ ,$\{z: \arg z = \theta, \theta\in E\}$ 恰好是其全体T方向和无穷级Borel方向的集合, 得到了关于无穷级亚纯函数与代数体函数的奇异方向的一个分布规律.Abstract: This paper explores the existence of infinite order meromorphic functions and algebroidal functions with given T directions. An algebroidal function$ \omega(z) $ of infinite order was constructed such that for an arbitrary given non-empty closed set of real numbers$ E\pmod {2\pi} $ ,$\{z: \arg z = \theta, \theta\in E\}$ is the set of all T directions and Borel directions of infinite order of$ \omega(z) $ ; using a method of cyclic values-assigned, the distribution of singular directions for meromorphic functions and algebroidal functions of infinite order is obtained.-
Key words:
- algebroidal function /
- infinite order /
- T direction /
- Borel direction
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