A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
Arithmetic diophantine approximation for continued fractions-like maps on the interval
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...
Efficient computation of addition chains
The aim of this paper is to present a unifying approach to the computation of short addition chains. Our method is based upon continued fraction expansions. Most of the popular methods for the generation of addition chains, such as the binary method, the factor method, etc..., fit in our framework. However, we present new and better algorithms. We give a general upper bound for the complexity of continued fraction methods, as a function of a chosen strategy, thus the total number of operations required...
Généralisation d'une famille de Shanks
Modular relations and explicit values of Ramanujan-Selberg continued fractions.
Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.
On Shanks' algorithm for computing the continued fraction of .
On the Maximal Lévy-Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
We prove that the sums of independent random vectors satisfy , t ≥ 0.
Products and quotients of numbers with small partial quotients
For any positive integer let denote the set of numbers with all partial quotients (except possibly the first) not exceeding . In this paper we characterize most products and quotients of sets of the form .
Ramanujan's cubic continued fraction revisited
Řetězové zlomky s předepsanou periodou
Článek se zabývá řetězovými zlomky algebraických čísel stupně 2. Jsou ukázány jejich základní vlastnosti, včetně potřebné teorie. Ta je poté použita k nalezení tvaru řetězového zlomku druhých odmocnin z přirozených čísel, které nejsou čtverce, a jejich symetrické posloupnosti . Dále, pro danou symetrickou posloupnost přirozených čísel jsou charakterizována všechna přirozená čísla, jejichž druhé odmocniny mají řetězový zlomek právě s touto symetrickou posloupností. Tato přirozená čísla jsou popsána...
Some methods for evaluating the regulator of a real quadratic function field.
Some results concerning certain periodic continued fractions
The determination of parabolic points in modular and extended modular groups by continued fractions.
Transformation homographique appliquée à un développement en fraction continue fini ou infini
Unisequences and nearest integer continued fraction midpoint criteria for Pell's equation.
Vyprávění o dvou sítech