6 papers
A Liouville-Type Inequality for Values of Mahler M-Functions
Boris Adamczewski, Colin Faverjon
We establish a Liouville-type inequality for the values, at a common nonzero algebraic point, of arbitrary Mahler Mq-functions. As an application, we prove that no such value is a…
A purity theorem for Mahler equations
Colin Faverjon, Julien Roques
The principal aim of this paper is to establish a purity theorem for Mahler functions that is reminiscent of famous purity theorems for G-functions by D. and G. Chudnovsky and for…
Computing basis of solutions of any Mahler equation
Colin Faverjon, Marina Poulet
Mahler equations arise in a wide range of contexts including the study of finite automata, regular sequences, algebraic series over Fp(z), and periods of Drinfeld modules. Introduc…
Regular singular Mahler equations and Newton polygons
Colin Faverjon, Marina Poulet
Though Mahler equations have been introduced nearly one century ago, the study of their solutions is still a fruitful topic for research. In particular, the Galois theory of Mahler…
Algebraic Independence Measures for Values of E-functions and M-functions
Colin Faverjon, Boris Adamczewski
In this article, we establish a Liouville-type inequality for polynomials evaluated at the values of arbitrary Siegel E-functions at non-zero algebraic points. Additionally, we pro…
Hahn series and Mahler equations: Algorithmic aspects
C. Faverjon, Julien Roques
Many articles have recently been devoted to Mahler equations, partly because of their links with other branches of mathematics such as automata theory. Hahn series (a generalizatio…