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arXiv:1901.01383 [math.NT]AbstractReferencesReviewsResources

Bounds on the period of the continued fraction after a Möbius transformation

Hanka Řada, Štěpán Starosta

Published 2019-01-05Version 1

We study M\"obius transformations (also known as linear fractional transformations) of quadratic numbers. We construct explicit upper and lower bounds on the period of the continued fraction expansion of a transformed number as a function of the period of the continued fraction expansion of the original number. We provide examples that show that the bound is sharp.

Comments: 42 pages
Categories: math.NT
Subjects: 11Y65, 11A55
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