Unimodular Invariance of Karyon Expansions of Algebraic Numbers in Multidimensional Continued Fractions
- 作者: Zhuravlev V.1,2
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隶属关系:
- V. A. Steklov Mathematical Institute of the RAS
- Vladimir State University
- 期: 卷 242, 编号 4 (2019)
- 页面: 531-559
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242999
- DOI: https://doi.org/10.1007/s10958-019-04494-5
- ID: 242999
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详细
By the method of differentiation of induced toric tilings, periodic expansions for algebraic irrationalities in multidimensional continued fractions are found. These expansions give the best karyon approximations with respect to polyhedral norms. The above irrationalities are obtained by the composition of backward continued fraction mappings and unimodular transformations of algebraic units that are expanded in purely periodic continued fractions. Karyon expansions have several invariants: recurrence relations for the numerators and denominators of the convergents of continued fractions and the rate of multidimensional approximation of irrationalities by rational numbers.
作者简介
V. Zhuravlev
V. A. Steklov Mathematical Institute of the RAS; Vladimir State University
编辑信件的主要联系方式.
Email: vzhuravlev@mail.ru
俄罗斯联邦, Moscow; Vladimir