On the algebraic relations between Mahler functions

2016/04/14 by Julien Roques · 6 citations
Computer Science · Mathematics · #semigroups and automata theory #Coding theory and cryptography #Advanced Combinatorial Mathematics

paper · pdf · doi:10.1090/tran/6945

Abstract

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 study in detail the equations of order <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and compute the difference Galois groups of classical equations related to the Baum-Sweet and to the Rudin-Shapiro automatic sequences.

Cited by

• Difference Riccati equations and Mahler method
• A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations
• A purity theorem for Mahler equations
• Computing basis of solutions of any Mahler equation
• Mahler's method in several variables I: The theory of regular singular systems
• On the computation of the difference Galois groups of order three equations

Related

• Computing basis of solutions of any Mahler equation
• Mahler equations for Zeckendorf numeration
• A purity theorem for Mahler equations
• Zero order estimates for Mahler functions
• Mahler's method in several variables II: Applications to base change problems and finite automata