CARMA OANT Seminar

3:00 pm

Monday, 15th Oct 2012

V206, Mathematics Building


A/Prof. Michael Coons

(CARMA, The University of Newcastle)

The rational-transcendental dichotomy of Mahler functions

In this talk, we will show that a D-finite Mahler function is necessarily rational. This 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. This is joint work with Jason Bell and Eric Rowland.