English

On a periodic Jacobi-Perron type algorithm

Number Theory 2021-02-17 v2

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.

Cite

@article{arxiv.2101.12627,
  title  = {On a periodic Jacobi-Perron type algorithm},
  author = {Oleg Karpenkov},
  journal= {arXiv preprint arXiv:2101.12627},
  year   = {2021}
}

Comments

59 pages

R2 v1 2026-06-23T22:39:31.417Z