The Rational-Transcendental Dichotomy of Mahler Functions
Jason P. Bell
Department of Mathematics
Simon Fraser University
School of Mathematical and Physical Sciences
The University of Newcastle
Université du Québec à Montréal
In this paper, we give a new proof of a result due to
Bézivin 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 Pólya-Carlson type result for Mahler
functions due to Randé; that is, a Mahler function which is
meromorphic in the unit disk is either rational or has the unit circle
as a natural boundary.
Full version: pdf,
(Concerned with sequence
Received July 3 2012;
revised version received October 2 2012.
Published in Journal of Integer Sequences, March 2 2013.
Journal of Integer Sequences home page