Proper cyclic symmetries of multidimensional continued fractions-Reference-Cited by-同舟云学术

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Proper cyclic symmetries of multidimensional continued fractions

Published:2022 Issue:9 Volume:213 Page:1290-1317
ISSN:1064-5616
Container-title:Sbornik: Mathematics
language:en
Short-container-title:Sb. Math.

Author:

Tlyustangelov Ibragim Aslanovich¹²

Affiliation:

1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

2. Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

Abstract

We show that palindromic continued fractions exist in an arbitrary dimension. For dimension $n=4$ we also prove a criterion for an algebraic continued fraction to have a proper cyclic palindromic symmetry. Klein polyhedra are considered as multidimensional generalizations of continued fractions. Bibliography: 11 titles.

Funder

Russian Science Foundation

Foundation for the Development of Theoretical Physics and Mathematics BASIS

Publisher

Steklov Mathematical Institute

Subject

Algebra and Number Theory

Reference14 articles.

1. Ueber eine geometrische Auffassung der gewöhnlichen Kettenbruchentwicklung;F. Klein;Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl.,1895

2. Additions au mémoire sur la résolution des équations numériques;J.-L. Lagrange;Mem. Acad. Roy. Sci. et Belles-lettres de Berlin,1770

3. Palindromes and periodic continued fractions;O. N. German and I. A. Tlyustangelov;Mosc. J. Comb. Number Theory,2016

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