Approximation by Nearest Integer Continued Fractions (II).
Approximation of values of hypergeometric functions by restricted rationals
We compute upper and lower bounds for the approximation of hyperbolic functions at points
Automates et fractions continues
Automatic continued fractions are transcendental or quadratic
We establish new combinatorial transcendence criteria for continued fraction expansions. Let be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients of is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.
Charles Hermite’s stroll through the Galois fields
Although everything seems to oppose the two mathematicians, Charles Hermite’s role was crucial in the study and diffusion of Évariste Galois’s results in France during the second half of the nineteenth century. The present article examines that part of Hermite’s work explicitly linked to Galois, the reduction of modular equations in particular. It shows how Hermite’s mathematical convictions—concerning effectiveness or the unity of algebra, analysis and arithmetic—shaped his interpretation of Galois...
Class Number Two for Real Quadratic Fields of Richaud-Degert Type
2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination...
Combinatorial aspects of the sequence of Milnor numbers of deformations
We use combinatorics to describe the topology of a singular irreducible plane curve germ f = 0 under small perturbation of parameters.
Comportement local moyen de la fonction de Brjuno
We describe the average behaviour of the Brjuno function Φ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of Φ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of Φ.
Consecutive powers in continued fractions
Construction de fractions continues périodiques uniformément bornées
Nous construisons, dans les corps quadratiques réels, une infinité de fractions continues périodiques uniformément bornées, avec une borne qui semble meilleure que celle connue jusqu’ici. Nous faisons cela en partant de développements en fractions continues de la même forme que ceux des réels . Et ceci nous permet d’obtenir de plus qu’il existe une infinité de corps quadratiques contenant une infinité de développements en fractions continues périodiques formées seulement des entiers et . Nous...
Construction of families of long continued fractions.
Continued fractions and Catalan problems.
Continued fractions and class number two.
Continued fractions and density results for Dedekind sums.
Continued fractions and the Gauss map.
Continued fractions, Fibonacci numbers, and some classes of irrational numbers.
Continued fractions for finite sums
Continued fractions of period five and real quadratic fields of class number one
Continuous fractions and reduced algebraic formal power series. (Fractions continues et séries formelles algébriques réduites.)
Convergents of folded continued fractions