The last years have seen a growing interest from mathematicians in Mahler functions. This
class of functions includes the generating series of the automatic sequences. The present …

We consider systems of linear differential and difference equations δY (x)= A (x) Y (x), σY
(x)= B (x) Y (x) with δ= d dx, σ a shift operator σ (x)= x+ a, the q-dilation operator σ (x)= qx or …

Any algebraic (resp. linear) relation over Q (z) between given analytic functions f1 (z),..., fn
(z)∈ Q {z} 1, leads by specialisation at a given algebraic point α to an algebraic (resp …

We develop a new method for proving algebraic independence of $ G $-functions. Our
approach rests on the following observation: $ G $-functions do not always come with a …

We develop a theory of linear Mahler systems in several variables from the perspective of
transcendence and algebraic independence, which also includes the possibility of dealing …

Cette note est consacrée aux aspects algorithmiques de la méthode de Mahler. Dans un
travail récent, nous avons utilisé un résultat de Philippon pour montrer qu'étant donnés une …

We consider pairs of automorphisms.;/acting on fields of Laurent or Puiseux series: pairs of
shift operators. W x 7! x C h1; W x 7! x C h2/, of q-difference operators. W x 7! q1x, W x 7 …

Suppose that is a Mahler function and that is in the radius of convergence of for an integer.
In this paper, we consider the approximation of by algebraic numbers. In particular, we prove …

We present a new method for algebraic independence results in the context of Mahler's
method. In particular, our method uses the asymptotic behavior of a Mahler function as goes …

We prove that all algebraic relations over $\overline {\mathbb Q} $ between values of
Siegel's $ E $-functions at some non-zero algebraic point have a functional source, in that …