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

JOURNAL OF NUMBER THEORY

卷:212

Article

Rada, Hanka¹  Starosta, Stepan² 

[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Prague, Czech Republic

[2] Czech Tech Univ, Fac Informat Technol, Prague, Czech Republic

关键词: Continued fraction;    Continued fraction period;    Mobius transformation;    Linear fractional transformation;   

DOI  :  10.1016/j.jnt.2019.10.027

来源: Elsevier

【 摘 要 】

Text. We study Mobius 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. Video. For a video summary of this paper, please visit https://youtu.be/je7WkmmZloc. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free