An extension of Picard's theorem for meromorphic functions of small hyper-order
An extension of Picard's theorem for meromorphic functions of small hyper-order
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DOI：
10.1016/j.jmaa.2009.04.011
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发表时间：
2009-03
影响因子：
1.3
通讯作者：
R. Korhonen
中科院分区：
文献类型：
--
作者：
R. Korhonen
证明了Nevanlinna理论的第二个主要定理的一个版本，其中分支项被替换为依赖于小超阶亚纯函数的某个复合算子的项。作为这一结果的推论，证明了：如果n∈N且超阶小于1/n2的亚纯函数f的三个不同值关于常系数代数函数τ（z）=z+αn− 1 z1 −1/n+ α n +α 1 z1/n+α 0的固定分支具有前向不变的原像，则f○τ <$f.这是Picard定理在小超阶亚纯函数中的推广，因为通常Picard例外值的（空）原像是前向不变原像的特殊情况。
A version of the second main theorem of Nevanlinna theory is proved, where the ramification term is replaced by a term depending on a certain composition operator of a meromorphic function of small hyper-order. As a corollary of this result it is shown that if n∈N and three distinct values of a meromorphic function f of hyper-order less than 1/n2have forward invariant pre-images with respect to a fixed branch of the algebraic function τ(z)=z+αn−1z1−1/n+⋯+α1z1/n+α0with constant coefficients, then f○τ≡f. This is a generalization of Picard's theorem for meromorphic functions of small hyper-order, since the (empty) pre-images of the usual Picard exceptional values are special cases of forward invariant pre-images.