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On the algebraic relations between Mahler functions

Author: Julien Roques
Journal: Trans. Amer. Math. Soc. 370 (2018), 321-355
MSC (2010): Primary 39A06, 12H10
Published electronically: July 13, 2017
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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 $ 2$ and compute the difference Galois groups of classical equations related to the Baum-Sweet and to the Rudin-Shapiro automatic sequences.

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Additional Information

Julien Roques
Affiliation: Institut Fourier, Université Grenoble 1, CNRS UMR 5582, 100 rue des Maths, BP 74, 38402 St. Martin d’Hères, France
Address at time of publication: Université Grenoble Alpes, Institut Fourier, CNRS UMR 5582, CS 40700, 38058 Grenoble Cedex 09, France

Keywords: Linear difference equations, difference Galois theory
Received by editor(s): April 10, 2015
Received by editor(s) in revised form: March 21, 2016
Published electronically: July 13, 2017
Article copyright: © Copyright 2017 by the author

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