复合函数方程的超越亚纯解

利用亚纯函数Nevanlinna值分布理论,研究了一类复合函数方程和一类复合函数方程组的超越亚纯解的性质问题,得到了2个有关复合函数方程和复合函数方程组当给予其系数的极点控制时,其解的特征估计和计数估计,将Silvennoinen的某些结果推广至更为复杂的复合函数方程和复合函数方程组中.举例表明定理中的条件是精确的.

The Transcendental Meromorphic Solutions of Composite Functional Equations

Using the Nevanlinna theory of the value distribution of meromorphic functions,the problem of properties of transcendental solutions of(systems of )composite functional equations are investigated,and characteristic estimate and non-integrated counting estimate of solutions are obtained while restricting the number of the poles of the coefficients,a certain result of Silvennoinen concerning composite functional equations is extened to systems of composite functional equations.Examples show that our condition in Theorems are precise.