作　　者： ; ;

机构地区： 广州航海学院

出　　处： 《华南师范大学学报（自然科学版）》 2019年第2期110-116,共7页

摘　　要： 研究了复平面上和单位圆内的不可约的有限正级代数体函数的Borel方向和确定该代数体函数的系数函数的Borel方向间的关系:通过巧妙构造扇形和单位圆之间的保形变换,应用Nevanlinna基本定理,结合涉及系数函数的Valiron特征,在考察代数体函数与其系数函数的增长性的基础上,得到了2个有趣的定理;证明了复平面上的有限正级的整代数体函数的系数函数的p级Borel方向必然是代数体函数本身的至少p级的Borel方向,而单位圆内的有限正级的代数体函数的p级Borel点必然是某个系数函数的至少p级的Borel方向. The relationship between the Borel directions of irreducible finite positive order algebroid functions and the Borel directions of their coefficient functions on the complex plane and in the unit circle was investigated. By constructing conformal transformation between the sector and the unit circle and using Nevanlinna s theory and Valiron characteristic of coefficient functions,two interesting theorems of Borel directions of algebroid functions were proved on the basis of investigating the growth of algebroid function and its coefficient function. It is proved that a p -order Borel direction of the coefficient functions of a finite positive order integral algebroid function on the complex plane must be a Borel direction of the algebroid function of at least order p . In the unit circle,a p -order Borel point of a finite positive order algebroid function must be a Borel direction of a coefficient function of at least order p .

关 键 词： 代数体函数 系数函数 增长级 方向

领　　域： []