6 citations · 22 across the 11 of their papers we have counts for
11 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…
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…
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…
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…
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…
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…
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…
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…
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…