涉及例外函数的亚纯函数正规定则与Picard型定理的研究

正规族与值分布理论是单复变函数论中的重要研究领域，其在亚纯函数的唯一性、复解析动力系统和复微分方程等方面有着广泛的应用。我们将深入研究以下两个方面的内容：1.探索涉及例外函数的亚纯函数（拟）正规定则。此外，对于拟正规定则，函数族在不正规点处的性质也是我们研究的重要内容；2.研究（拟）正规族理论在亚纯函数值分布理论中应用，应用（拟）正规定则建立涉及例外函数的Picard型定理。我们拟以球面平均覆盖次数代替球面导数去建立正规定则和Picard型定理之间的联系。我们希望在研究方法和技巧上有所突破和创新，为正规族和值分布理论的研究开辟一条新的道路，丰富和完善已有的结果。

Normal family and value distribution theory of meromorphic functions are an important research in the functions of one complex variable, which has been widely used in uniqueness of meromorphic functions, complex dynamical systems and complex differential equations. We will deeply study the following two aspects: 1.Explore the (quasi)normal criterions of meromorphic functions concerning the exceptional functions. In addition, for quasinormal criterions, the properties of function families at the non-normal points are also important contents of our research; 2.Study the application of (quasi) normal family theory in meromorphic function value distribution theory and establish Picard-type theorem involving exceptional functions with the application of (quasi) normal criterions. We intend to replace the spherical derivative with the average number of spherical covers to establish the connection between normal criterions and Picard-type theorem. We hope to make breakthroughs and innovations in research methods and techniques, so as to open up a new path for the research of normal family and value distribution theory and enrich and perfect the existing results.