含四个未知函数的费马型丢番图函数方程非平凡亚纯解的研究

摘要

本文利用亚纯函数值分布论的思想方法,对费马型丢番图函数方程fn1(z)+n2f(z)+fn3(z)+fn4(z)=1的非平凡亚纯解的存在状况进行研究,得到如下结果:函数方程f171(z)f172(z)f173(z)f174(z)=1不存在级小于1的非常数亚纯函数解.%This paper based on the value distribution theory of meromorphic function, carries out a systematical study on the solutions of Diophantine functional equation f_1~n (z)+f~_2~n (z)+f_3~n (z)+f, (z)=l. In the paper, we will obtain a result as feEow: There is no nonconstant meromorphic functional solutions with order smaller than one satisfying the equation f_1~17 (z)+f_2~17 (z)+f_3~17 (z)+f_4~17 (z)=l.