# CARMA OANT Seminar

## 3:00 pm

## Monday, 15^{th} 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.