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The group structure for ζ(3)
1. Introduction. In his proof of the irrationality of ζ(3), Apéry [1] gave sequences of rational approximations to ζ(2) = π 2 /6 and to ζ(3) yielding the irrationality measures µ(ζ(2)) < 11.85078. ..Expand
Approximants de Padé et mesures effectives d’irrationalité
Les approximants de Pade; des fonctions hypergeometriques ont ete utilises pour l’etude en des points rationnels z=p/q des approximations diophantiennes des valeurs de ces fonctions. Cette methodeExpand
Approximants de Padé simultanés de logarithmes
Resume Les approximants de Pade simultanes de logarithmes fournissent des approximations rationnelles simultanees de logarithmes de certains nombres rationnels proches de 1. Ils permettent d'obtenirExpand
The integer transfinite diameter of intervals and totally real algebraic integers
In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals + 03B4], is a fixed rationalExpand
On the absolute Mahler measure of polynomials having all zeros in a sector
Let α be an algebraic integer of degree d, not 0 or a root of unity, all of whose conjugates α i are confined to a sector |arg z| ≤ θ. We compute the greatest lower bound c(θ) of the absolute MahlerExpand
Two families of periodic Jacobi Algorithms with period lengths going to infinity
We exhibit two infinite families of periodic Jacobi Algorithm expansions with period length equal to 4m+1 in the first case and to 3m+1 in the second case.
Integer transfinite diameter and polynomials with small Mahler measure
In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in C give very good bounds for coefficients of polynomials with small Mahler measure. ByExpand
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best pre- viously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying ourExpand