函数方程f15(z)+g15(z)+h15(z)+w15(z)=1的亚纯函数解的研究

The Study of Meromorphic Function Solution of Function Equation of f15(z)+g15(z)+h15(z)+w15(z)=1

本文证明了若非常数亚纯函数f(z),g(z),h(z),w(z)的极点中至多只有一个是公共单级极点,且min{ρf,ρg,ρh,ρw}<1/2,则f(z),g(z),h(z),w(z)一定不是Fermat型函数方程f15(z)+g15(z)+h15(z)+w15(z)=1的解。

This paper proves that nonconstant meromorphic function f (z), g (z),h(z),w(z) in the pole is not more than a single pole with public, and min{ρf,ρg,ρh,ρw}<1/2 , the solution of Fermat function equations f15 (z) + g15 (z) + h15 (z) + w15(z) =1 does not exist.