Odd-odd continued fraction algorithm

By using a jump transformation associated to the Romik map, we define a new continued fraction algorithm called odd-odd continued fraction, whose principal convergents are rational numbers of odd denominators and odd numerators. Among others, it is proved that all the best approximating rationals of...

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Bibliographic Details
Published inarXiv.org
Main Authors Dong Han Kim, Seul Bee Lee, Liao, Lingmin
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.12.2020
Subjects
Algorithms
Convergence
Irrationality
Mathematics - Dynamical Systems
Mathematics - Number Theory
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Summary:By using a jump transformation associated to the Romik map, we define a new continued fraction algorithm called odd-odd continued fraction, whose principal convergents are rational numbers of odd denominators and odd numerators. Among others, it is proved that all the best approximating rationals of odd denominators and odd numerators of an irrational number are given by the principal convergents of the odd-odd continued fraction algorithm and vice versa.
ISSN:2331-8422
DOI:10.48550/arxiv.2002.06310