本文对n≥3时,函数方程fn(z)+gn(z)=1没有非常数整函数解的结果给出新的证明。
In this paper, a new proof is given for the result that if n≥3, there are no non-constant entire so-lutions of the functional equation fn(z)+gn(z)=1.
Fermat型函数方程,整函数,正规族理论, Fermat Type Functional Equation Entire Functions Normal Families Theory关于Fermat型函数方程的整函数解
1985年W. K. Hayman [1] 证明了:当时,方程(2)不存在非常数亚纯解;当时,方程(2)不存在非常数整函数解。此外,当时,G. G. Gundersen [2] - [4] 等人找到了满足方程(2)的非常数整函数解;当时,G. G. Gundersen [5] 构造了满足方程(2)的非常数亚纯解。
段江梅,苏 敏. 关于Fermat型函数方程的整函数解 Entire Solutions of Fermat Type Functional Equations[J]. 理论数学, 2016, 06(02): 116-120. http://dx.doi.org/10.12677/PM.2016.62017
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