摘要翻译:
在20世纪20年代,Ritt研究了复有理函数上的泛函组合g o h(x)=g(h(x))的运算。在多项式的情况下,他描述了多项式在这个运算中可以有多重“素因子分解”的所有方式。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进展甚微。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次幂的有理函数。
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英文标题:
《Decompositions of Laurent polynomials》
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作者:
Michael E. Zieve
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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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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PDF链接:
https://arxiv.org/pdf/0710.1902