Linear-Fractional Invariance of Multidimensional Continued Fractions
- Authors: Zhuravlev V.G.1
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Affiliations:
- Vladimir State University
- Issue: Vol 234, No 5 (2018)
- Pages: 616-639
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241965
- DOI: https://doi.org/10.1007/s10958-018-4033-4
- ID: 241965
Cite item
Abstract
The invariance of the simplex-karyon algorithm for expanding real numbers α = (α1, …, αd) in multidimensional continued fractions under linear-fractional transformations \( {\alpha}^{\prime }=\left({\alpha}_1^{\prime },\dots, {\alpha}_d^{\prime}\right)=U\left\langle \alpha \right\rangle \) with matrices U from the unimodular group GLd+1(ℤ) is established. For the transformed collections α′, convergents of the best approximations are found.
About the authors
V. G. Zhuravlev
Vladimir State University
Author for correspondence.
Email: vzhuravlev@mail.ru
Russian Federation, Vladimir