An arithmetic criterion for the values of the exponential function
An axiomatization of Nesterenko's method and applications on Mahler functions II
Applications of differential algebra to algebraic independence of arithmetic functions
We generalize and unify the proofs of several results on algebraic independence of arithmetic functions and Dirichlet series by using a theorem of Ax on the differential Schanuel conjecture. Along the way, we find counter-examples to some results in the literature.
Approximation algébrique en caractéristique p
Approximation diophantienne et indépendance algébrique de logarithmes
Arithmetic properties of automata: regular sequences.
Arithmetic properties of certain power series with algebraic coefficients
Arithmetic properties of the solutions of a class of functional equations.
Arithmetical properties of gap series with algebraic coefficients
Arithmetische Eigenschaften spezieller Heinescher Reihen.
Character coordinates and annihilators of cyclotomic 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
Correction to my paper: Arithmetic properties of certain power series with algebraic coefficents
Corrections to “How to explicitly solve a Thue-Mahler equation”
Critères pour l'indépendance algébrique
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Effective estimates for global relations on Euler-type series
Effective measures for algebraic independence of the values of Mahler type functions
Ein Approximationsmaß für transzendente Lösungen gewisser transzendenter Gleichungen.