【摘要】 目的研究亚纯函数在角域内的值分布，亏值亏量与Ｎｅｖａｎｌｉｎｎａ方向及其它奇异方向．方法使用Ｎｅｖａｎｌｉｎｎａ特征函数在角域的一个基本不等式，它类似于Ｎｅｖａｎｌｉｎｎａ第二基本定理．结果给出亚纯函数关于角域及一个方向的亏值亏量概念，改进Ｎｅｖａｎｌｉｎｎａ方向的定义．结论对于一类亚纯函数证明亏值至多为可数个，且亏量总和不超过２．证明Ｎｅｖａｎｌｉｎｎａ方向的存在性．还得到亚纯函数的Ｂｏｒｅｌ方向与Ｊｕｌｉａ方向的存在性以及它们之间的关系更多还原

【Abstract】 Aim To study the value distribution of meromorphic functions in angular domains, the deficiency, the deficient value, the Nevanlinna direction and other singular directions. Methods A fundamental inequality of Nevanlinna characteristic functions in the angular domain was used, which is similar with the Nevanlinna secondary fundamental theorem. Results The deficiency and deficient value of meromorphic functions about an angular domain and a direction were defined. The definition of Nevanlinna direction was improved. Conclusion For a family of meromorphic functions, it is proved that the number of deficient values is at most countable and the sum of deficiencies isnt greater than 2. The existence of the Nevanlinna direction is obtained. The existence of Borel and Julia directions and the relation between them are found.更多还原