Arithmetic properties of the solutions of a class of functional equations.
Arithmetical properties of gap series with algebraic coefficients
Arithmetische Eigenschaften ganzer Funktionen mehrerer Variablen.
Arithmetische Eigenschaften spezieller Heinescher Reihen.
Automates et valeurs de transcendance du logarithme de Carlitz
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.
Beweis der Transcendenz der Zahl e.
Beweis der Transcendenz der Zahl e
Calculs sur des suites récurrentes linéaires
Comments on some formulae of Ramanujan
Complete systems of addition laws on Abelian varieties.
Computing the lower bound for linear forms in logarithms
Conditions for algebraic independence of certain power series of algebraic numbers
Conjecture de Schanuel sur la transcendance d'exponentielles
Constructive and non-constructive methods of proofs of irrationality and transcendency and algebraic independence of periods of abelian varieties
Continued fractions and transcendental numbers
The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].
Continued Fractions of Transcendental Numbers
Contributions to the theory of transcendental numbers (I)
Contributions to the theory of transcendental numbers (II)
Correction to my paper: Arithmetic properties of certain power series with algebraic coefficents