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Acta Arithmetica

### A geometric proof to Cantor's theorem and an irrationality measure for some Cantor's series.

Annales Mathematicae et Informaticae

Acta Arithmetica

### A note to the transcendence of special infinite series

Mathematica Slovaca

### A powerful determinant.

Experimental Mathematics

### À propos de la série $\sum _{n=1}^{+\infty }\frac{{x}^{n}}{{q}^{n}-1}$

Journal de théorie des nombres de Bordeaux

Acta Arithmetica

### Algebraic independence of the generating functions of Stern’s sequence and of its twist

Journal de Théorie des Nombres de Bordeaux

Very recently, the generating function $A\left(z\right)$ of the Stern sequence ${\left({a}_{n}\right)}_{n\ge 0}$, defined by ${a}_{0}:=0,{a}_{1}:=1,$ and ${a}_{2n}:={a}_{n},{a}_{2n+1}:={a}_{n}+{a}_{n+1}$ for any integer $n>0$, has been considered from the arithmetical point of view. Coons  proved the transcendence of $A\left(\alpha \right)$ for every algebraic $\alpha$ with $0<|\alpha |<1$, and this result was generalized in  to the effect that, for the same $\alpha$’s, all numbers $A\left(\alpha \right),{A}^{\prime }\left(\alpha \right),{A}^{\prime \prime }\left(\alpha \right),...$ are algebraically independent. At about the same time, Bacher  studied the twisted version $\left({b}_{n}\right)$ of Stern’s sequence, defined by ${b}_{0}:=0,{b}_{1}:=1,$ and ${b}_{2n}:=-{b}_{n},{b}_{2n+1}:=-\left({b}_{n}+{b}_{n+1}\right)$ for any $n>0$.The aim of our paper is to show...

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

### Approximation diophantienne et distances ultramétriques non standard

Annales de la Faculté des sciences de Toulouse : Mathématiques

### Approximation measures for logarithms of algebraic numbers

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### Approximations to $q$-logarithms and $q$-dilogarithms, with applications to $q$-zeta values.

Journal of Mathematical Sciences (New York)

### Arithmetical investigations of a certain infinite product

Compositio Mathematica

### Birational transformations and values of the Riemann zeta-function

Journal de théorie des nombres de Bordeaux

In his proof of Apery’s theorem on the irrationality of $\zeta \left(3\right)$, Beukers [B] introduced double and triple integrals of suitable rational functions yielding good sequences of rational approximations to $\zeta \left(2\right)$ and $\zeta \left(3\right)$. Beukers’ method was subsequently improved by Dvornicich and Viola, by Hata, and by Rhin and Viola. We give here a survey of our recent results ([RV2] and [RV3]) on the irrationality measures of $\zeta \left(2\right)$ and $\zeta \left(3\right)$ based upon a new algebraic method involving birational transformations and permutation groups...

### Complément à : «Sur l’approximation de $\pi$ par des nombres algébriques particuliers»

Compositio Mathematica

### Continued Fractions for Some Alternating Series.

Monatshefte für Mathematik

### Convergents and irrationality measures of logarithms.

Revista Matemática Iberoamericana

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