亚纯函数值分布论与几何函数论均是复分析中的主要研究领域，在这些领域中仍有一些复分析学者比较关注的一些问题没有解决。例如，几何函数论中关于多项式临界点分布的Sendov 猜想、亚纯函数论中关于整函数（或亚纯函数）唯一性像集的最小基数精确值问题和费尔马型丢番图函数方程的非平凡整函数（或亚纯函数）解的存在性问题等均没有彻底解决。对这些问题的深入研究对于丰富和发展几何函数论与亚纯函数值分布论具有重要的意义。本项目拟研究的主要问题是：.（1）、多项式的临界点与零点相对位置关系的Sendov 猜想；.（2）、整函数、亚纯函数CM型唯一性像集的最小基数的精确值问题；.（3）、含三个未知函数的费尔马型丢番图函数方程非平凡整函数（亚纯函数）解的存在性问题。.本项目将争取在对上述问题的研究取得实质性的进展乃至解决其中的一些问题。

Meromorphic function value distribution theoey and geometric function theory are.both of main filed of complex analysis, in these fields still has many interest open problems, For example, Sendov conjecture in geometric function theory, does there existence of non-trival entire function (or meromorphic function) solutions of some Fermat type Diophantine functional equations, and the precise value of minimu cardinal number of CM type uniqueness range sets of entire functions (or meromorphic functions) are not solved yet. To investigate these open problems can abundant and .expand meromorphic function theory and geometric function theory.. In this project, we will stuty the following problems:. (1). The Sendov conjecture of polynomials.. (2). The problem to find the precise value of minimum cardinal number of CM . type uniqueness range sets of entire functions (or meromorphic functions).. (3). The problem to determine the existence of non-trival entire function (or .meromorphic function) solutions of some Fermat type Diophantine functional .equations which contain three unknow functions.. To investigate above three problems, we try to get essence progress even solve some problems.