Value distribution与线性算子
Value distribution and linear operators
摘要：
Nevanlinna的第二个主要定理是一个深远的推广皮卡德定理有关的价值分布的任意亚纯函数f。该定理采用包含导数项的不等式的形式，其中导数f'的零点和极点出现。在本文中，我们证明了一个类似的结果适用于亚纯函数的特殊子域，其中的导数被替换为一个更一般的线性算子，如高阶微分算子和微分-差分算子。随后，我们得到推广的皮卡德定理和缺陷的关系。
英文摘要：
Nevanlinna's second main theorem is a far-reaching generalisation of Picard's Theorem concerning the value distribution of an arbitrary meromorphic function f. The theorem takes the form of an inequality containing a ramification term in which the zeros and poles of the derivative f' appear. In this paper we show that a similar result holds for special subfields of meromorphic functions where the derivative is replaced by a more general linear operator, such as higher-order differential operators and differential-difference operators. We subsequently derive generalisations of Picard's Theorem and the defect relations.
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