On a periodic Jacobi-Perron type algorithm

被引：0

作者：

Karpenkov, Oleg ^{[1
]}

机构：

[1] Univ Liverpool, Liverpool, England

来源：

MONATSHEFTE FUR MATHEMATIK | 2024年 / 205卷 / 03期

关键词：

Jacobi-Perron algorithm; Klein continued fractions; Dirichlet group;

D O I：

10.1007/s00605-024-02006-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1848 Ch. Hermite formulated a question on periodic representation of cubic numbers. In this paper we introduce a new Jacobi-Perron type algorithm that provides periodicity for all cubic irrationalities in the input and prove the periodicity. This is the first subtractive algorithm for which the algebraic periodicity is proven. The algorithm is designed for the totally real case, providing the answer to Hermite's original question in this case.

引用

页码：531 / 601

页数：71

共 50 条

[31] GENERALIZATION OF THE JACOBI-PERRON ALGORITHM FOR COMPUTATION OF THE NUMBER OF INTEGER POINTS IN THE POLYTOPES
ZAMANSKY, LY
CHERKASSKY, VL
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1985, (10): : 10 - 13
[32] THE QUALITY OF THE DIOPHANTINE APPROXIMATIONS FOUND BY THE JACOBI-PERRON ALGORITHM AND RELATED ALGORITHMS
LAGARIAS, JC
MONATSHEFTE FUR MATHEMATIK, 1993, 115 (04): : 299 - 328
[33] RATIONAL APPROXIMATIONS OF ALGEBRAIC IRRATIONALS BY MEANS OF A MODIFIED JACOBI-PERRON ALGORITHM
BERNSTEIN, L
DUKE MATHEMATICAL JOURNAL, 1965, 32 (01) : 161 - +
[34] The exponent of convergence for 2-dimensional Jacobi-Perron type algorithms
Nakaishi, K
MONATSHEFTE FUR MATHEMATIK, 2001, 132 (02): : 141 - 152
[35] The Exponent of Convergence for 2-Dimensional Jacobi-Perron Type Algorithms
Kentaro Nakaishi
Monatshefte für Mathematik, 2001, 132 : 141 - 152
[36] On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups
Karpenkov, Oleg
ACTA ARITHMETICA, 2022, 203 (01) : 27 - 48
[37] Continued fraction algorithms and Jacobi-Perron algorithms
Adam, B
Rhin, G
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1996, 53 (02) : 341 - 350
[38] JACOBI-PERRON ALGORITHM IN NUMBER-FIELDS OF 4TH-DEGREE
BOUHAMZA, M
ACTA ARITHMETICA, 1984, 44 (02) : 141 - 145
[39] UNIT CALCULATION IN CUBIC BODIES USING JACOBI-PERRON ALGORITHM FROM COMPUTER
BERNSTEIN, L
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1970, 244 : 201 - +
[40] Discrete planes, Z2-actions, Jacobi-Perron algorithm and substitutions
Arnoux, P
Berthé, V
Ito, S
ANNALES DE L INSTITUT FOURIER, 2002, 52 (02) : 305 - +

← 1 2 3 4 5 →