使用重复矩阵形式的一般多维续分数的周期性

IF 0.8 4区数学 Q2 MATHEMATICS Expositiones Mathematicae Pub Date : 2024-04-04 DOI:10.1016/j.exmath.2024.125571

Hanka Řada , Štěpán Starosta , Vítězslav Kala

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引用次数: 0

摘要

我们考虑用一般的多维续分算法对向量进行展开。如果扩展最终是周期性的，那么我们就描述了与重延对应的矩阵的可能结构，并用它来证明一些向量在代数雅各比-珀伦算法中具有最终周期性扩展。此外，我们还给出了向量具有纯周期性展开的标准；特别是，向量不能是全正的。

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Periodicity of general multidimensional continued fractions using repetend matrix form

We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend and use it to prove that a number of vectors have an eventually periodic expansion in the Algebraic Jacobi–Perron algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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