On the algebraic relations between Mahler functions
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- by Julien Roques PDF
- Trans. Amer. Math. Soc. 370 (2018), 321-355
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.References
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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
- MR Author ID: 803167
- Email: Julien.Roques@univ-grenoble-alpes.fr
- Received by editor(s): April 10, 2015
- Received by editor(s) in revised form: March 21, 2016
- Published electronically: July 13, 2017
- © Copyright 2017 by the author
- Journal: Trans. Amer. Math. Soc. 370 (2018), 321-355
- MSC (2010): Primary 39A06, 12H10
- DOI: https://doi.org/10.1090/tran/6945
- MathSciNet review: 3717982