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arXiv · 1901.01383

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

Hanka Řada·Štěpán Starosta
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Abstract

We study Möbius 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.

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Hanka Řada, Štěpán Starosta. 2019-01-05. Bounds on the period of the continued fraction after a Möbius transformation. https://doi.org/10.1016/j.jnt.2019.10.027

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