Hayman猜想的新研究与复微分差分方程

本项目以Hayman猜想、复微分差分方程、Fermat型方程为依托，利用经典与差分Nevanlinna理论结合指数型函数性质、椭圆函数理论为主要研究工具，是项目团队前期研究的几个重要问题的深入创新，将继续攻关复微分差分Hayman猜想、首次开展成对型Hayman猜想研究、研究复微分差分方程及其退化方程亚纯函数解的性质、攻关Fermat型差分或微分差分方程亚纯函数解的性质，问题新颖，创新拓展空间广阔。. 本项目指数型函数研究能改善涉及差分值分布研究时超级小于1的限制；成对型Hayman猜想是研究思路上的重要创新，能衍生很多唯一性或正规性研究问题，具有重要科研引领作用；复微分差分或Fermat型方程也备受关注正处于研究的关键时期。. 项目团队已具有较好研究基础，具备科研实力，通过本项目必可获得一些重要成果，给值分布和函数方程的研究注入新活力，能促进复微分差分领域和值分布理论的重要发展。

In this project, we will consider some problems concerning to Hayman conjecture, complex differential-difference equations, Fermat type equations by using classical and difference Nevanlinna theory, the properties of exponential type functions and elliptic functions. These problems are the innovative researches based on our foundation. We will explore complex differential-difference Hayman conjecture, construct a pairwise Hayman conjecture, investigate the properties on meromorphic solutions on complex differential-difference equations and special equations, consider Fermat difference or differential-difference equations. These problems are novel and full of innovation and expansion.. The investigation on exponential type functions can improve the restriction of hyper-order less than one when considering value distribution of complex difference; the pairwise Hayman conjecture is an important innovation on research ideas, which can bring some new problems on uniqueness and normal families. Complex differential-difference equations and Fermat equations are in a critical research period.. The applicant and members have good research foundation on this project and have good research ability. We believe that we can get some significant results in this project to bring new energy on value distribution and complex functional equations and to make important developments on these topics.