关于Fermat 型函数方程的亚纯解

本文研究了三项Fermat 型函数方程亚纯解的存在性问题, 证明了: 如果(1/n) + (1/m) + (1/k) < (25/72) ; 则不存在非常数亚纯函数f, g, h 满足函数方程fⁿ + g^m + h^k ≡ 1:

On meromorphic solutions of Fermat type functional equations

In this paper,we investigate the existence of meromorphic solutions of three terms Fermat type functional equations,and prove that there do not exist non-constant meromorphic functions f（z）,g（z） and h（z） that satisfy the functional equation fn ＋ gm ＋ hk ≡ 1,provided that n1 ＋ m1 ＋ k1 7225,where n,m and k are positive integers.