论文标题
指数多项式的价值分布及其在复杂微分方程和振荡理论的理论中的作用
Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory
论文作者
论文摘要
指数多项式是$ p（z）e^{q（z）} $的有限线性总和，其中$ p（z）$和$ q（z）$是多项式。指数多项式的价值分布的早期结果可以追溯到1920年发表的乔治·帕利亚（GeorgPólya）的论文，而最新的结果在2021年出现。尽管有一个多世纪的研究工作，许多关于指数性多项式价值分布的有趣问题仍未解决。还将讨论指数多项式及其商在线性/非线性微分方程理论中，振荡理论和差分差方程的作用。提出了十三个开放问题，以激发读者在这些主题中进行进一步研究。
An exponential polynomial is a finite linear sum of terms $P(z)e^{Q(z)}$, where $P(z)$ and $Q(z)$ are polynomials. The early results on the value distribution of exponential polynomials can be traced back to Georg Pólya's paper published in 1920, while the latest results have come out in 2021. Despite of over a century of research work, many intriguing problems on value distribution of exponential polynomials still remain unsolved. The role of exponential polynomials and their quotients in the theories of linear/non-linear differential equations, oscillation theory and differential-difference equations will also be discussed. Thirteen open problems are given to motivate the readers for further research in these topics.
