Geodesic
Fractional-linear invariance of multidimensional continued fractions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 42-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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With the help of the simplex-karyon algorithm it is possible to decompose real numbers $\alpha=(\alpha_1,\dots,\alpha_d)$ into multidimensional continued fractions. We prove the invariance of this algorithm under fractional-linear transformations $\alpha'=(\alpha'_1,\dots,\alpha'_d)=U\langle\alpha\rangle$ with matrices $U$ from the unimodular group $\mathrm{GL}_{d+1}(\mathbb Z)$. The best convergent fractions of the transformed $\alpha'$ are found. 
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     author = {V. G. Zhuravlev},
     title = {Fractional-linear invariance of multidimensional continued fractions},
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     year = {2017},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a4/}
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V. G. Zhuravlev. Fractional-linear invariance of multidimensional continued fractions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 42-76. http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a4/

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