The rational-transcendental dichotomy of Mahler functions

Host Institution:

University of Newcastle

Title of Seminar:

The rational-transcendental dichotomy of Mahler functions

Speaker's Name:

Dr Michael Coons

Speaker's Institution:

CARMA, University of Newcastle

Time and Date:

Monday 15 October, 3.00pm (EST)

Seminar Abstract:

CARMA/SigmaOpt/OCANA Seminar

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.

 

Seminar Convenor:

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