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arXiv · 2002.06310

Odd-odd continued fraction algorithm

Dong Han Kim·Seul Bee Lee·Lingmin Liao
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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.

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Dong Han Kim, Seul Bee Lee, Lingmin Liao. 2020-12-19. Odd-odd continued fraction algorithm. https://doi.org/10.1007/s00605-022-01704-2

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