Sur la nature arithmétique des valeurs de fonctions modulaires
Sur les fonctions monodromes et les nombres transcendants
The digamma function, Euler-Lehmer constants and their p-adic counterparts
The goal of this article is twofold. First, we extend a result of Murty and Saradha (2007) related to the digamma function at rational arguments. Further, we extend another result of the same authors (2008) about the nature of p-adic Euler-Lehmer constants.
Transcendance et fonctions modulaires
Cette rédaction contient l'exposé fait aux Journées Arithmétiques 97 et une annexe concernant la méthode de Mahler. Le début de l'exposé présente les notions mises en jeu dans le cœur du sujet (courbes elliptiques et formes modulaires). Pour un traitement complet de ces notions on peut se référer à [Ser], [Lan1] et [Lan2]. Une preuve complète du théorème de Yuri Nesterenko se trouve, en dehors de l'article original ([Nes1] pour l'annonce et [Nes2] pour les démonstrations), dans les exposés de Michel...
Transcendence of the values of functions satisfying generalized Mahler type functional equations.
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...
Transcendency of Local Conjugacies in Complex Dynamics and Transcendency of their Values.
Transcendental values of the p-adic digamma function
Transcendentality of zeros of higher derivatives of functions involving Bessel functions.
Two theorems on meromorphic functions used as a principle for proofs on irrationality
In this paper we discuss two theorems on meromorphic functions of Nikishin and Chudnovsky. Our purpose is to show, how to derive some well-known but not obvious results on irrationality in a systematic and simple way from properties of meromorphic functions with arithmetic conditions. As far as it stands, we have no new results on irrationality, to the contrary some results on numbers of the corollaries are known already since a long time to be transcendental (cf. [4], [9] and [10]). Our main intention...
Utilisation de la conjugaison complexe dans l’étude de la transcendance de valeurs de la fonction exponentielle usuelle
Ce texte illustre l’usage que l’on peut faire de la conjugaison complexe en transcendance. Il montre aussi que la dérivation et le principe du maximum ne sont pas toujours des outils indispensables dans les preuves de transcendance. Ces deux constatations mises côte a côte permettront peut être de traiter quelques cas particuliers de la conjecture de Schanuel.
Verscharfung eines Arithmetischen Satzes von Tschakaloff
Werte hypergeometrischer Funktionen.
Zero order estimates for functions satisfying generalized functional equations of Mahler type
Zur Transzendenz von Lückenreihen mit ganzalgebraischen Koeffizienten und algebraischem Argument
Zwei Bemerkungen über transzendente Zahlen.
Критерий алгебраической независимости значений одного класса гипергеометрических E-функций
Линейные формы от значений G-функций и диофантовы уравнения
О линейной независимости значений целых гипергеометрических функций с иррациональными параметрами