Linear recurrence sequences and periodicity of multidimensional continued fractions
Linear recurrence sequences and periodicity of multidimensional continued fractions
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线性递推序列和多维连分数的周期性
DOI：
10.1007/s11139-016-9820-2
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Nadir Murru
中科院分区：
文献类型：
--
作者：
Nadir Murru
多维连分式推广了经典的连分式，目的是通过整数序列提供代数无理性的周期表示。利用线性递归序列刻画了Jacobi-Perron算法的周期性。特别地，我们证明了多维连分式的部分商是周期的当且仅当收敛的分子和分母是线性递归序列，推广了经典连分式的类似结果。
Multidimensional continued fractions generalize classical continued fractions with the aim of providing periodic representations of algebraic irrationalities by means of integer sequences. We provide a characterization for periodicity of Jacobi–Perron algorithm by means of linear recurrence sequences. In particular, we prove that partial quotients of a multidimensional continued fraction are periodic if and only if numerators and denominators of convergents are linear recurrence sequences, generalizing similar results that hold for classical continued fractions.