On the continued fractions of quadratic surds
On the length of continued fractions representing a rational number with given denominator
On the length of the continued fraction for values of quotients of power sums
Generalizing a result of Pourchet, we show that, if are power sums over satisfying suitable necessary assumptions, the length of the continued fraction for tends to infinity as . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers , .
On the length of the period of ...d.
On the Lengths of the Periods of the Continued Fractions of Square-Roots of Integers.
On the period length of some special continued fractions
We investigate and refine a device which we introduced in [3] for the study of continued fractions. This allows us to more easily compute the period lengths of certain continued fractions and it can be used to suggest some aspects of the cycle structure (see [1]) within the period of certain continued fractions related to underlying real quadratic fields.
On the quasi-periodic -adic Ruban continued fractions
We study a family of quasi periodic -adic Ruban continued fractions in the -adic field and we give a criterion of a quadratic or transcendental -adic number which based on the -adic version of the subspace theorem due to Schlickewei.
On the Ramanujan AGM fraction. II: The complex-parameter case.
On the statistical properties of finite continued fractions.
Orderings of the rationals and dynamical systems
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...
Orthogonal polynomials and Ramanujan's -continued fractions.
Periodic Jacobi-Perron expansions associated with a unit
We prove that, for any unit in a real number field of degree , there exits only a finite number of n-tuples in which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for . For we give an explicit algorithm to compute all these pairs.
Periodicity of p-adic continued fractions.
Periodizitätseigenschaften p-adischer Kettenbrüche.
Polynomial continued fractions
Polynomials of Pellian Type and Continued Fractions
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex-...
Portraits of Numbers
Poznámka o řetězcích
Příspěvek k nauce o nekonečných řetězcích
Příspěvek k nauce o zlomcích řetězových neb řetězcích