Rational approximations to linear forms in values of G-functions
Rational approximations to π and some other numbers
Simultaneous approximation to a real number and to its cube by rational numbers
Sur l’approximation de par des nombres algébriques particuliers
Sur le diamètre transfini entier d'un intervalle à extrémités rationnelles
Dans cet article nous améliorons des encadrements connus du diamètre transfini entier d’intervalles dont les bornes sont deux éléments consécutifs d’une suite de Farey. Nous verrons comment la majoration du diamètre transfini de tels intervalles dépend de la minoration de certaines mesures de polynômes unitaires, à coefficients entiers et totalement positifs, mesures qui généralisent la longueur usuelle. D’autre part, appliquant un lemme classique sur les résultants à une famille de polynômes totalement...
The group structure for ζ(3)
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best previously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying our permutation group method to the diophantine study of double integrals of rational functions related to the dilogarithm.
The Rhin-Viola method for log 2
Thue's Fundamentaltheorem, I: The general case
Transcendence measure for η/ω
Transcendence measures for continued fractions involving repetitive or symmetric patterns
There is a long tradition in constructing explicit classes of transcendental continued fractions and especially transcendental continued fractions with bounded partial quotients. By means of the Schmidt Subspace Theorem, existing results were recently substantially improved by the authors in a series of papers, providing new classes of transcendental continued fractions. It is the purpose of the present work to show how the Quantitative Subspace Theorem yields transcendence measures for (most of)...
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets
This article continues two papers which recently appeared in this same journal. First, Dilcher and Stolarsky [140 (2009)] introduced two new power series, F(z) and G(z), related to the so-called Stern polynomials and having coefficients 0 and 1 only. Shortly later, Adamczewski [142 (2010)] proved, inter alia, that G(α),G(α⁴) are algebraically independent for any algebraic α with 0 < |α| < 1. Our first key result is that F and G have large blocks of consecutive zero coefficients. Then, a Roth-type...
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II
This article continues a previous paper by the authors. Here and there, the two power series F(z) and G(z), first introduced by Dilcher and Stolarsky and related to the so-called Stern polynomials, are studied analytically and arithmetically. More precisely, it is shown that the function field ℂ(z)(F(z),F(z⁴),G(z),G(z⁴)) has transcendence degree 3 over ℂ(z). This main result contains the algebraic independence over ℂ(z) of G(z) and G(z⁴), as well as that of F(z) and F(z⁴). The first statement is...
Über lineare Unabhängigkeit.
Une nouvelle minoration de |logα - β|, |α - expβ|, α et β algébriques
Une version quantitative du théorème de Lindemann-Weierstrass
Values of meromorphic functions of order 2
Values of polynomials with integer coefficients and distance to their common zeros
Zur Transzendenz der Werte der Exponentialfunktion.
Об оценках мер алгебраической независимости значений E- функций.