Odd-odd continued fraction algorithm

Dong Han Kim; Seul Bee Lee; Lingmin Liao

doi:10.1007/s00605-022-01704-2

Odd-odd continued fraction algorithm

Dong Han Kim, Seul Bee Lee, Lingmin Liao

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	323-344
Number of pages	22
Journal	Monatshefte fur Mathematik
Volume	198
Issue number	2
DOIs	https://doi.org/10.1007/s00605-022-01704-2
State	Published - Jun 2022

Keywords

Continued fractions
Diophantine approximation
Romik system

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10.1007/s00605-022-01704-2

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Odd-odd continued fraction algorithm

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Keywords

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