arXiv Open Access 2020

Symmetries of a two-dimensional continued fraction

Oleg N. German Ibragim A. Tlyustangelov

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Abstrak

In this paper we describe the group of symmetries of a two-dimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: the Dirichlet-type ones, that correspond to the multiplication by units of the corresponding number field, and so called palindromic ones. The main result of the paper is a criterion for a two-dimensional continued fraction to have a palindromic symmetry. This criterion is analogous to the criterion for the period of a quadratic irrationality to be symmetric.

Topik & Kata Kunci

math.NT

Penulis (2)

Oleg N. German

Ibragim A. Tlyustangelov

Format Sitasi

APA MLA BibTeX

German, O.N., Tlyustangelov, I.A. (2020). Symmetries of a two-dimensional continued fraction. https://arxiv.org/abs/2007.02831

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓