Algebraic independence of Mahler functions and their values

Algebraic Independence of Mahler Functions via Radial Asymptotics

We present a new method for algebraic independence results in the context of Mahler’s method. In particular, our method uses the asymptotic behaviour of a Mahler function f(z) as z goes radially to a root of unity to deduce algebraic independence results about the values of f(z) at algebraic numbers. We apply our method to the canonical example of a degree two Mahler function; that is, we apply...

Algebraic Independence of Values of Elliptic Functions

On the Algebraic Independence of the Values of E - Functions

Algebraic independence of functions satisfying certain Mahler type functional equations and its applications

One of the techniques used to prove the algebraic independence of numbers is Mahler’s method, which deals with the values of so-called Mahler functions satisfying a certain type of functional equation. In order to apply the method, one must confirm the algebraic independence of the Mahler functions themselves. This can be reduced, in many cases, to their linear independence modulo the rational ...

On the Algebraic Relations between Mahler Functions

In the last years, a number of authors have studied the algebraic relations between the generating series of automatic sequences. It turns out that these series are solutions of Mahler type equations. This paper is mainly concerned with the difference Galois groups of Mahler type equations (these groups reflect the algebraic relations between the solutions of the equations). In particular, we s...