Unimodular Invariance of Karyon Expansions of Algebraic Numbers in Multidimensional Continued Fractions

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 composi...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2019-10, Vol.242 (4), p.531-559
Main Author: Zhuravlev, V. G.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Norms
Numbers
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04494-5