Unimodular Invariance of Karyon Expansions of Algebraic Numbers in Multidimensional Continued Fractions
- Авторы: Zhuravlev V.1,2
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Учреждения:
- V. A. Steklov Mathematical Institute of the RAS
- Vladimir State University
- Выпуск: Том 242, № 4 (2019)
- Страницы: 531-559
- Раздел: 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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Аннотация
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.
Об авторах
V. Zhuravlev
V. A. Steklov Mathematical Institute of the RAS; Vladimir State University
Автор, ответственный за переписку.
Email: vzhuravlev@mail.ru
Россия, Moscow; Vladimir