【摘要】 该文应用Ahlfors覆盖曲面理论研究了涉及离散值的亚纯函数的正规定理.首先定义了亚纯函数的单叶离散值,然后深入考察了 Ahlfors关于岛的不等式,得到两个关于岛的精密不等式.最后应用所得到的不等式研究了亚纯函数的离散值和正规族,得到了一个涉及单叶岛的正规定理和一个涉及单叶离散值的正规定理,这些定理推广了著名的Ahlfors五岛定理与Nevanlinna五单值定理.更多还原

【Abstract】 In this paper,the normal theorems of meromorphic functions involving discrete values are studied by using the theory of Ahlfors covering surfaces.Firstly,the discrete values with one leaf of meromorphic functions are defined,then the inequalities about islands are investigated and two precise inequalities about islands are obtained.Finally,the inequalities are used to study the discrete values and the normal family of meromorphic functions,then a normal theorem involving a monophyletic island and a normal theorem involving discrete values of one leaf are obtained.All these theorems promote the famous Ahlfors’ five islands theorem and five single valued theorem of Nevanlinna.更多还原