Email this article Simplex-Module Algorithm for Expansion of Algebraic Numbers in Multidimensional Continued Fractions
- Authors: Zhuravlev V.G.1
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Affiliations:
- V. A. Steklov Mathematical Institute of the Russian Academy of Sciences
- Issue: Vol 225, No 6 (2017)
- Pages: 924-949
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239867
- DOI: https://doi.org/10.1007/s10958-017-3506-1
- ID: 239867
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Abstract
The simplex-module algorithm for expansion of algebraic numbers α = (α1, . . . , αd) in multidimensional continued fractions is suggested. The method is based on minimal rational simplices s, where α ∈ s, and Pisot matrices Pα, for which \( \widehat{\alpha} \) = (α1, . . . , αd, 1) is an eigenvector. A multidimensional generalization of the Lagrange theorem is proved.
About the authors
V. G. Zhuravlev
V. A. Steklov Mathematical Institute of the Russian Academy of Sciences
Author for correspondence.
Email: vzhuravlev@mail.ru
Russian Federation, Moscow
