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

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