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Conjecture de Littlewood et récurrences linéaires

Bernard de Mathan (2003)

Journal de théorie des nombres de Bordeaux

Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples ( α , β ) de nombres réels à constantes de Markov finies, tels que 1 , α et β soient 𝐙 -linéairement indépendants, et satisfaisant à la conjecture de Littlewood.

Continued fraction expansions for complex numbers-a general approach

S. G. Dani (2015)

Acta Arithmetica

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

Boris Adamczewski, Yann Bugeaud, Les Davison (2006)

Annales de l’institut Fourier

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 on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey (2015)

Acta Arithmetica

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.

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