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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 458, Pages 42–76
(Mi znsl6453)
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This article is cited in 3 scientific papers (total in 3 papers)
Fractional-linear invariance of multidimensional continued fractions
V. G. Zhuravlev Vladimir State University, Vladimir, Russia
Abstract:
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.
Key words and phrases:
multidimensional continued fractions, the best approximations, Farey summs.
Received: 05.04.2017
Citation:
V. G. Zhuravlev, “Fractional-linear invariance of multidimensional continued fractions”, Analytical theory of numbers and theory of functions. Part 33, Zap. Nauchn. Sem. POMI, 458, POMI, St. Petersburg, 2017, 42–76; J. Math. Sci. (N. Y.), 234:5 (2018), 616–639
Linking options:
https://www.mathnet.ru/eng/znsl6453 https://www.mathnet.ru/eng/znsl/v458/p42
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Abstract page: | 140 | Full-text PDF : | 46 | References: | 31 |
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