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Journal of Algebra 319 (2008) 23372350 www.elsevier.com/locate/jalgebra

Summary: Journal of Algebra 319 (2008) 2337­2350
Function fields in positive characteristic:
Expansions and Cobham's theorem
Boris Adamczewski a,
, Jason Bell b
a CNRS, Université de Lyon, Université Lyon 1, Institut Camille Jordan, Bât. Braconnier, 21 avenue Claude Bernard,
69622 Villeurbanne Cedex, France
b Department of Mathematics, Simon Fraser University, 8888, University Drive, Burnaby, BC V5A 1S6, Canada
Received 11 October 2006
Available online 30 January 2008
Communicated by Eva Bayer-Fluckiger
In the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a problem of
Mahler for rational functions in positive characteristic. To solve this question, we prove an extension of
Cobham's theorem for quasi-automatic functions and use the recent generalization of Christol's theorem
obtained by Kedlaya.
© 2008 Elsevier Inc. All rights reserved.
Keywords: Automatic sequences; Cobham's theorem; Christol's theorem; Hahn's power series
1. Introduction


Source: Adamczewski, Boris - Institut Camille Jordan, Université Claude Bernard Lyon-I


Collections: Mathematics