亚纯函数与其函数位移及差分算子分担公共值问题的研究

The project intends to use Nevanlinna theory of meromorphic functions to investigate shared value problems related to a meromorphic function with its shift, or with its difference operator. Based on difference counterparts of Nevanlinna theory, we will seek some new crossing points between value distribution theory，complex differential equations and complex difference equations. Furthermore, we will try to look for a general way to solve the problems in difference counterparts of Nevanlinna theory. The study of this project is the cross-over study between Nevanlinna theory and complex difference equations, and is an interesting subject of complex analysis recently. This project is devoted to Nevanlinna theory’s connections and applications in difference theory, and to improving some recent results within the field of uniqueness theory of meromorphic functions. In this project, we mainly continue to study the related proplems of shared value by some innovative research methods, which can be positive in the developments and connectons in different branch of mathematics.

申请者拟利用Nevanlinna理论研究亚纯函数及其函数位移，差分算子的分担值问题。本项目将在Nevanlinna理论的基础上，寻求不同理论间新的交叉点，希望通过对亚纯函数值分布理论、复微分方程、复差分方程等理论的深入探究，找到解决相关差分问题的一般途径和方法，争取得到几个比较理想的结果。本项目的研究是Nevanlinna理论和复差分理论的交叉研究，是近几年来复分析方向比较活跃的研究领域，是一个富有意义的课题。对此项目的研究，目的在于丰富近几年来不断发展的差分Nevanlinna理论的内涵，精确亚纯函数与其函数位移，差分算子分担公共值的结果，创新研究方法，进一步深入研究相关问题，这对复分析的发展、探索和促进不同数学分支间的交叉都很有意义。

通过一年的项目执行期，项目组成员不仅按照申请书的计划，具体研究了亚纯函数及其函数位移，差分算子的分担值问题。并且以本项目为依托，对复差分方程的解的存在性，增长级等相关性质同样进行了研究。除此之外，我们还讨论了复差分（ 阶差分）多项式分担公共值问题，得到了一系列结果。与本项目有关的研究结果，以论文的形式在国内外学术期刊发表7篇，接收1篇。 其中SCI收录期刊5篇，核心期刊2篇，全部标注基金。