On a periodic Jacobi-Perron type algorithm

2021/01/29 by Oleg Karpenkov, Karpenkov, Oleg · 2 citations
Engineering · Mathematics · #11A05 #11H99 #11R16 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2101.12627

openalex publication_date 2021/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a new modification of the Jacobi-Perron algorithm in three dimensional case and prove its periodicity for the case of totally-real conjugate cubic vectors. This provides an answer in the totally-real case to the question son algebraic periodicity for cubic irrationalities posed in 1849 by Ch.~Hermite.

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