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

作者：Vincze Csaba^*

来源：Periodica Mathematica Hungarica, 2017, 74(1): 112-117.

DOI：10.1007/s10998-016-0171-y

• Algebraic dependent systems
• Polynomials
• Linear functional equations
• Spectral analysis
• Characteristic polynomials of linear functional equations

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.

• 出版日期2017-3