谐波三项式的埃格瓦利定理

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-02-15 DOI:10.1007/s10474-024-01403-4

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引用次数: 0

摘要

摘要我们研究了被称为谐波三项式的裂隙谐波多项式在复平面上的根的排列。我们提供了必要条件和充分条件，使两个一般的谐波三项式在复平面内绕原点旋转、在实轴上反射或前两种变换的组合时具有相同的根集。这将 Jenő Egerváry 在 [19] 中给出的三项式结果扩展到了调和三项式。

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Egerváry's theorems for harmonic trinomials

Abstract

We study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficient conditions so that two general harmonic trinomials have the same set of roots up to a rotation around the origin in the complex plane, a reflection over the real axis, or a composition of the previous both transformations. This extends the results of Jenő Egerváry given in [19] for the setting of trinomials to the setting of harmonic trinomials.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.