Publications (14)
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…
Relations algébriques entre valeurs de E-fonctions ou de M-fonctions
Boris Adamczewski, Colin Faverjon
We prove that all algebraic relations over between values of Siegel's -functions at some non-zero algebraic point have a functional source, in that they c…
Mahler's method in several variables I: The theory of regular singular systems
Boris Adamczewski, Colin Faverjon
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two m…
Addendum to: Mahler's method in several variables and finite automata
Colin Faverjon, Boris Adamczewski
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
A new proof of Nishioka's theorem in Mahler's method
Boris Adamczewski, Colin Faverjon
In a recent work [3], the authors established new results about general linear Mahler systems in several variables from the perspective of transcendental number theory, such as a m…
Méthode de Mahler, transcendance et relations linéaires : aspects effectifs
Boris Adamczewski, Colin Faverjon
This note deals with some effective results in Mahler's method. In a recent work, we used a theorem of Philippon to show that given a Mahler function in , wher…
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…
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…
An algorithm to recognize regular singular Mahler systems
Colin Faverjon, Marina Poulet
This paper is devoted to the study of the analytic properties of Mahler systems at 0. We give an effective characterisation of Mahler systems that are regular singular at 0, that i…
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…
Mahler's method in several variables and finite automata
Boris Adamczewski, Colin Faverjon
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 w…
Méthode de Mahler: relations linéaires, transcendance et applications aux nombres automatiques
Boris Adamczewski, Colin Faverjon
This paper is concerned with Mahler's method. We study in detail the structure of linear relations between values of Mahler functions at algebraic points. In particular, given a fi…
Mahler's method in several variables II: Applications to base change problems and finite automata
Boris Adamczewski, Colin Faverjon
This is the second part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. From the lift…
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…