Diophantine approximation of Mahler numbers

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
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