亚纯函数正规族及其若干问题的研究

项目名称： 亚纯函数正规族及其若干问题的研究

项目编号： No.11461070

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 田宏根

作者单位： 新疆师范大学

项目金额： 40万元

中文摘要： 亚纯函数理论是复分析中的一个重要分支，亚纯函数值分布是我国在世界上具有领先水平的数学分支之一，它的理论已经渗透到数学的很多分支和领域。正规族理论是研究复分析中问题的一个有力工具，我们将运用覆盖曲面等理论，结合传统分析方法深入研究亚纯函数的正规理论，试图寻找新的正规定则，尤其是代数体函数的正规理论；并探索新的研究手段，希望在研究方法和技巧上有所突破和创新，进而丰富和完善亚纯函数的值分布理论。级数是一类特殊的亚纯函数，随机级数是结合复分析与概率的一门边缘学科，我们将在前人研究的基础上深入研究Dirichlet级数和随机Dirichlet级数的增长性；同时研究一般随机变量的随机级数，注重对离散型随机级数、慢增长随机级数及随机级数下级的研究。将亚纯函数值分布、增长性等理论应用到复方程上，力求取得好的成果。

中文关键词： 亚纯函数；值分布；正规族；级数；复方程

英文摘要： Meromorphic function theory is an important branch of complex analysis. The value distribution of meromorphic functions, in which China is leading at a higher level in the world, has penetrated into many areas of mathematics. Normal family theory is a powerful tool to study complex analysis problems. By covering surface theory and traditional analysis methods, we will deeply research formal theory of meromorphic functions and try to find some new normal criteria, especially the normal theory of algebroid functions. In order to enrich and perfect the value distribution theory of meromorphic function, we will explore new research means, break through and innovate research methods and skills. Series is a special meromorphic function,while random series is an edge subject which combines with complex analysis and probability. On the basis of previous studies, the growth of Dirichlet series and random Dirichlet growth and Random series of general random variables will be studied. We will pay attention to study of the lower order of discrete random series and random series of slow growth and random series, apply the value distribution of meromorphic functions and the growth theory to complex equation and try to get good results.

英文关键词： meromorphic funcntions;value distribution;normal families;series;complex equation