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The parabola theorem on continued fractions

Short, Ian (2016). The parabola theorem on continued fractions. Computational Methods and Function Theory, 16(4) pp. 653–675.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s40315-016-0164-0
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Abstract

Using geometric methods borrowed from the theory of Kleinian groups, we interpret the parabola theorem on continued fractions in terms of sequences of Möbius transformations. This geometric approach allows us to relate the Stern–Stolz series, which features in the parabola theorem, to the dynamics of certain sequences of Möbius transformations acting on three-dimensional hyperbolic space. We also obtain a version of the parabola theorem in several dimensions.

Item Type: Journal Item
Copyright Holders: 2016 Springer-Verlag
ISSN: 1617-9447
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 45359
Depositing User: Ian Short
Date Deposited: 24 Feb 2016 14:46
Last Modified: 04 May 2019 07:23
URI: http://oro.open.ac.uk/id/eprint/45359
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