q移位差分方程的亚纯解及任意亚纯函数分担3个值的唯一性

Uniqueness of Meromorphic Solutions of q-Shift Difference Equations and Sharing Three Values of Any Meromorphic Functions

用Nevanlinna理论,研究差分方程a_1(z)f(qz+p)+a_0(z)f(z)=F(z)一个有穷级超越亚纯解f(z)及任一亚纯函数g(z)分担0,1,∞IM时的唯一性问题(其中p,q为常数,满足n∈N^+,q^n≠±1,q≠0,a_1(z),a_0(z),F(z)为非零亚纯函数且级均小于1),得到了f(z)=g(z).

By using Nevanlinna theory,we studied the uniqueness problem for difference equation a_1（z）f（qz＋p）＋a_0（z）f（z）=F（z）when a inite-order transcendental meromorphic solution f（z）and any meromorphic function g（z）were sharing 0,1,∞ IM（where q,p were constants,n∈ N~＋,q^n≠±1,q≠0,a_1（z）,a_0（z）,F（z）were nonzero meromorphic functions and the order was less than1）,we got the result f（z）=g（z）.