Journal of Mathematical Sciences

, Volume 234, Issue 5, pp 640–658 | Cite as

Linear-Fractional Invariance of the Simplex-Module Algorithm for Expanding Algebraic Numbers in Multidimensional Continued Fractions

  • V. G. ZhuravlevEmail author

The paper establishes the invariance of the simplex-module algorithm for expanding real numbers α = (α1, …, αd) in multidimensional continued fractions under linear-fractional transformations \( {\alpha}^{\prime }=\left({\alpha}_1^{\prime },\dots, {\alpha}_d^1\right)=U\left\langle \alpha \right\rangle \) with matrices U from the unimodular group GLd+1(ℤ). It is shown that the convergents of the transformed collections of numbers α satisfy the same recurrence relation and have the same approximation order.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vladimir State UniversityVladimirRussia

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