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On linear independence measures of the values of Mahler functions

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  22 June 2018

Keijo Väänänen  and
Wen Wu
Keijo Väänänen
Affiliation:
Department of Mathematical Science, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland ([email protected])
Wen Wu*
Affiliation:
School of Mathematics, South China University of Technology, Guangzhou 510641, People's Republic of China ([email protected])
*
*Corresponding author.
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Abstract

We estimate the linear independence measures for the values of a class of Mahler functions of degrees 1 and 2. For this purpose, we study the determinants of suitable Hermite–Padé approximation polynomials. Based on the non-vanishing property of these determinants, we apply the functional equations to get an infinite sequence of approximations that is used to produce the linear independence measures.

Keywords

linear formMahler functionHermite–Padé approximation

MSC classification

Primary: 11J13: Simultaneous homogeneous approximation, linear forms
Secondary: 11J72: Irrationality; linear independence over a field 39B32: Equations for complex functions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 6 , December 2018 , pp. 1297 - 1311
Copyright
Copyright © Royal Society of Edinburgh 2018 

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