给定Borel方向的代数体函数

The Algebroid Functions with Given Borel Directions

通常所说的代数体函数是指由不可约的二元复方程(1.1)确定的多值函数.由于二元复方程的可约性的验证存在难度且不可约的二元复方程在局部区域可能是可约的,因此该文研究了由一般二元复方程(不一定要求不可约)确定的代数体函数在圆盘内的基本性质,并应用这些性质构造了具有给定Borel方向的无穷级代数体函数.

Algebroid functions are multi-valued function that generally determined by the irreducible binary complex equations. There exists some difficulties in verifying the irreducible of such equations, and the irreducible binary complex equations may be reducible in the local domain. Hence in this paper, we investigate the properties of the algebroid functions defined by the binary complex equations （not necessarily irreducible） in the disc. And by using the obtained properties, we construct the infinite order algebroid functions with given Borel directions.