Periodicity of general multidimensional continued fractions using repetend matrix form
Autoři
Řada, H.; Starosta, Š.; Kala, V.
Rok
2024
Publikováno
EXPOSITIONES MATHEMATICAE. 2024, 42(3), ISSN 0723-0869.
Typ
Článek
Pracoviště
Anotace
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend and use it to prove that a number of vectors have an eventually periodic expansion in the Algebraic Jacobi–Perron algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive.
Matrix Form of Multidimensional Continued Fractions
Autoři
Rok
2022
Publikováno
Doktorandské dny 2022. Praha: CTU. Faculty of Nuclear Sciences and Physical Engineering, 2022. p. 113-124.
Typ
Stať ve sborníku
Pracoviště
Bounds on the period of the continued fraction after a Möbius transformation
Autoři
Rok
2020
Publikováno
Journal of Number Theory. 2020, 212 122-172. ISSN 0022-314X.
Typ
Článek
Pracoviště
Anotace
We study Möbius transformations (also known as linear fractional transformations) of quadratic numbers. We construct explicit upper and lower bounds on the period of the continued fraction expansion of a transformed number as a function of the period of the continued fraction expansion of the original number. We provide examples that show that the bound is sharp.