- Title
- The rational-transcendental dichotomy of Mahler functions
- Creator
- Bell, Jason P.; Coons, Michael; Rowland, Eric
- Relation
- Journal of Integer Sequences Vol. 16, p. 1-11
- Relation
- https://cs.uwaterloo.ca/journals/JIS/VOL16/Bell/bell2.html
- Publisher
- University of Waterloo, Department of Computer Science
- Resource Type
- journal article
- Date
- 2013
- Description
- In this paper, we give a new proof of a result due to Bèzivin 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.
- Subject
- Mahler function; finite automata; k -regular sequence
- Identifier
- http://hdl.handle.net/1959.13/1045111
- Identifier
- uon:14415
- Identifier
- ISSN:1530-7638
- Language
- eng
- Full Text
- Reviewed
- Hits: 2267
- Visitors: 2369
- Downloads: 179
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT02 | Publisher version (open access) | 143 KB | Adobe Acrobat PDF | View Details Download |