Linear recurrence sequences and periodicity of multidimensional continued fractions

被引:4
作者
Murru, Nadir [1 ]
机构
[1] Univ Turin, Dept Math, Via Carlo Alberto 10, I-10123 Turin, Italy
关键词
Algebraic irrationalities; Jacobi-Perron algorithm; Linear recurrence sequences; Multidimensional continued fractions; JACOBI-PERRON ALGORITHMS; CUBIC IRRATIONALITIES; EXPANSIONS; THEOREM; FAMILY; UNITS;
D O I
10.1007/s11139-016-9820-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:115 / 124
页数:10
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