辛克莱和瓦勒定理注解

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2020-01-01 DOI:10.7153/mia-2020-23-52

L. Losonczi

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引用次数: 1

摘要

辛克莱和瓦勒在[6]定理1.2中发现了自逆多项式在单位圆上全部为零的充分条件，即依赖于参数p1的系数是非线性的。这里我们讨论了条件对参数的依赖性，并通过它证明了应用Lakatos和Losonczi的定理1可以通过给出零点的位置来加强它们的结果。数学学科分类(2010):30C15、12D10、42C05。

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Remarks to a theorem of Sinclair and Vaaler

Sinclair and Vaaler in [6] Theorem 1.2 found sufficient conditions, nonlinear in the coefficients depending on a parameter p 1 , for self-inversive polynomials to have all their zeros on the unit circle. Here we discuss the dependence of the conditions on the parameter and through it we show that applying Theorem 1 of Lakatos and Losonczi [4] their result can be strengthened by giving the locations of the zeros. Mathematics subject classification (2010): 30C15, 12D10, 42C05.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.