| 麦结华,刘新和.多项式的根的一个性质的判定[J].数学研究及应用,2001,21(1):17~20 |
| 多项式的根的一个性质的判定 |
| On a Property of Roots of Polynomials |
| 投稿时间：1998-07-17 |
| DOI：10.3770/j.issn:1000-341X.2001.01.003 |
| 中文关键词: |
| 英文关键词:polynomial root functional iterative equation irrational rotation. |
| 基金项目: |
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| 摘要点击次数: 2312 |
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| 中文摘要: |
| 文献[1]在讨论多项式型的函数迭代方程的局部解析解的存在性时涉及到了多项式的根的一个性质.本文给出了判定该性质是否成立的一个简洁的条件，证明了多项式λnzn+…+λ2z2+λ1z+λ0有一个根α满足inf{｜λnαnm+…+λ2a2m+λ1αm+λ0｜：m=2，3，…｝>0当且仅当如下两个条件之中至少有一个成立：(i)该多项式有一个根β满足｜β｜>1；(ii)该多项式有一个根β满足｜β｜<1，且λ0≠0. |
| 英文摘要: |
| In [1], a property of roots of polynomials is considered, which involves the existence of local analytic solutions of polynomial-like functional iterative equations. In this paper we discuss this property and obtain a succinct condition to decide whether this property holds. Our main result is: A polynomial λnzn+…+λ2z2+λ1z+λ0 of degree n has a root α such that inf{｜λnαnm+…+λ2a2m+λ1αm+λ0｜：m=2，3，…｝>0 if and only if at least one of the following two conditions holds: (i) the polynomial has a root βsatisfying ｜β｜ ＞ 1; (ii) the polynomial has a root βsatisfying ｜β｜ < 1, and λ0 ≠ 0. |
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