- Title
- Diophantine approximation of Mahler numbers
- Creator
- Bell, Jason P.; Bugeaud, Yann; Coons, Michael
- Relation
- ARC.DE140100223 http://purl.org/au-research/grants/arc/DE140100223
- Relation
- Proceedings of the London Mathematical Society Vol. 110, Issue 5, p. 1157-1206
- Publisher Link
- http://dx.doi.org/10.1112/plms/pdv016
- Publisher
- Oxford University Press
- Resource Type
- journal article
- Date
- 2015
- Description
- Suppose that F(x) ∈ ℤ[x] is a Mahler function and that 1/b is in the radius of convergence of F(x) for an integer b ≥ 2. In this paper, we consider the approximation of F(1/b) by algebraic numbers. In particular, we prove that F(1/b) cannot be a Liouville number. If, in addition, F(x) is regular, we show that F(1/b) is either rational or transcendental, and in the latter case that F(1/b) is an S-number or a T-number in Mahler's classification of real numbers.
- Subject
- Mahler numbers; Diophantine approximation
- Identifier
- http://hdl.handle.net/1959.13/1339571
- Identifier
- uon:28287
- Identifier
- ISSN:0024-6115
- Language
- eng
- Reviewed
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