• Mathematics
  • Published 2012

The rational-transcendental dichotomy of Mahler functions

@inproceedings{Bell2012TheRD,
  title={The rational-transcendental dichotomy of Mahler functions},
  author={Jason P. Bell and Michael Coons and Eric Rowland},
  year={2012}
}
In this paper, we give a new proof of a result due to Bezivin that a D-finite Mahler function is necessarily rational. This also gives a new proof of the rational-transcendental dichotomy of Mahler functions due to Nishioka. Using our method of proof, we also provide a new proof of a Polya-Carlson type result for Mahler functions due to Rande; that is, a Mahler function which is meromorphic in the unit disk is either rational or has the unit circle as a natural boundary. 

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