Algebraic dependency of roots of multivariate polynomials and its applications to linear functional equations

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• 作者：Csaba Vincze
• 关键词：Algebraic dependent systems ; Polynomials ; Linear functional equations ; Spectral analysis ; Characteristic polynomials of linear functional equations
• 刊名：Periodica Mathematica Hungarica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：112-117
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1588-2829
• 卷排序：74

文摘

In this paper we prove that a multivariate polynomial has algebraically dependent roots if and only if the coefficients are algebraic numbers up to a common proportional term; for the problem see section 4.4 in Varga-Vincze (On the characteristic polynomials of linear functional equations, Period Math Hungar 71(2):250–260, 2015). The case of univariate polynomials belongs to basic algebra. As far as we know the case of multivariate polynomials is not discussed in the literature. As an application we formulate a sufficient and necessary condition for the existence of non-trivial solutions of special types of linear functional equations. The criteria is based only on the algebraic properties of the parameters in the functional equation.