解析函数的局部ABC定理
Local ABC theorems for analytic functions
摘要：
多项式的经典$abc$定理（通常称为梅森定理）处理方程$a+b=c$的非平凡多项式解。它提供了多项式$abc$的不同零的数目的下限，该下限表示为$°{a}$、$°{b}$和$°{c}$。证明了一般解析函数在合理有界区域$Ω\subset\mathbb C$上而不是在整个$\mathbb C$上的“局部”$abc$型定理.得到的估计是尖锐的，任何$Ω$，他们意味着（推广）原来的“全球”$abc$定理的限制参数。
英文摘要：
The classical $abc$ theorem for polynomials (often called Mason's theorem) deals with nontrivial polynomial solutions to the equation $a+b=c$. It provides a lower bound for the number of distinct zeros of the polynomial $abc$ in terms of $°{a}$, $°{b}$, and $°{c}$. We prove some "local" $abc$-type theorems for general analytic functions living on a reasonable bounded domain $Ω\subset\mathbb C$, rather than on the whole of $\mathbb C$. The estimates obtained are sharp, for any $Ω$, and they imply (a generalization of) the original "global" $abc$ theorem by a limiting argument.
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