费马型函数方程的亚纯解

数学理论与应用 ›› 2018, Vol. 38 ›› Issue (1-2): 33-37.

费马型函数方程的亚纯解

段江梅

昭通学院数学与统计学院

出版日期:2018-06-30 发布日期:2020-09-18

The Meromorphic Solution to Fermat Type Functional Equations

Online:2018-06-30 Published:2020-09-18

摘要/Abstract

摘要： 本文研究Fermat型函数方程亚纯解的存在性问题,证明函数方程f(z)⁷+f^(s)(z)⁷+h(z)⁷ =1不存在级小于1的非常数亚纯解.

关键词: 费马型函数方程, 亚纯函数, Nevanlinna理论

Abstract: In this paper,the meromorphic solution to Fermat type functional equations is investigated.We prove that there do not exist non-constant meromorphic functions f(z),f(s)(z)and h(z)with order less than one that satisfy the functional equation f(z)7+f(s)(z)7+h(z)7 =1.

Key words: Fermat type functional equation, Meromorphic functions , Nevanlinna theory

段江梅. 费马型函数方程的亚纯解[J]. 数学理论与应用, 2018, 38(1-2): 33-37.

Duan Jiangmei. The Meromorphic Solution to Fermat Type Functional Equations[J]. Mathematical Theory and Applications, 2018, 38(1-2): 33-37.