摘要
假设函数f(z)是亚纯函数,H(z,f)是关于f(z)的差分多项式,s(z)是关于f(z)的小函数,考察了差分多项式f(z)~nH(z,f)-s(z)的零点分布问题.首先得到了差分多项式f(z)~nH(z,f)-s(z)的零点计数函数和函数f(z)的特征函数以及极点计数函数之间的一些不等式估计,再根据这些不等式,建立了Hayman关于亚纯函数的一个经典结果的差分模拟.
In this paper, the authors investigate zeros of difference polynomials of the form f(z)~nH(z, f)-s(z), where f(z) is a meromorphic function, H(z,f) is a difference polynomial of f(z) and s(z) is a small function. The authors first obtain some inequalities for the relationship of the zero counting function of f(z)~nH(z,f)-s(z) and the characteristic function and pole counting function of f(z). Based on the above inequalities, the authors then establish some difference analogues of a classical result of Hayman for meromorphic functions.
引文
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