Laurent多项式的分解
Decompositions of Laurent polynomials
摘要：
在20世纪20年代，Ritt研究了复有理函数上的函数复合g o h（x）= g（h（x））的运算。在多项式的情况下，他描述了所有的方式，其中多项式可以有多个'素因子分解'关于这个操作。尽管Ritt和其他人做出了巨大的努力，但在解决有理函数的类似问题方面几乎没有取得进展。本文利用Avanzi-Zannier和Bilu-Tichy的结果证明了Ritt关于Laurent多项式分解的类似结果，即，分母为x的幂的有理函数。
英文摘要：
In the 1920's, Ritt studied the operation of functional composition g o h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple `prime factorizations' with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving the analogous problem for rational functions. In this paper we use results of Avanzi--Zannier and Bilu--Tichy to prove analogues of Ritt's results for decompositions of Laurent polynomials, i.e., rational functions with denominator a power of x.
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