关键词: 代数体函数, 无穷级, Borel方向

Abstract:

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.

Key words: Algebroid function, Infinite order, Borel direction