Characteristic approximation properties of quadratic irrationals.
Conjecture de Littlewood et récurrences linéaires
Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples de nombres réels à constantes de Markov finies, tels que et soient -linéairement indépendants, et satisfaisant à la conjecture de Littlewood.
Continuants with Bounded Digits - III.
Continued fraction expansions for complex numbers-a general approach
We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the absolute values...
Continued fractions and transcendental numbers
The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].
Continued fractions for some algebraic numbers.
Continued Fractions for Some Alternating Series.
Continued fractions, multidimensional diophantine approximations and applications
This paper is a brief review of some general Diophantine results, best approximations and their applications to the theory of uniform distribution.
Continued fractions of Laurent series with partial quotients from a given set
Continued Fractions of Transcendental Numbers
Continued fractions on the Heisenberg group
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
Convergence of Continued Fraction Type Algorithms and Generators.
Convergents of folded continued fractions
Correction to : “Linear fractional transformations of continued fractions with bounded partial quotients”
We fill a gap in the proof of a theorem of our paper cited in the title.