On linear independence measures of the values of Mahler functions

Keijo Väänänen; Wen Wu

doi:10.1017/S0308210518000148

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

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Keijo Väänänen: Affiliation:
Department of Mathematical Science, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland (keijo.vaananen@oulu.fi)
Wen Wu*: Affiliation:
School of Mathematics, South China University of Technology, Guangzhou 510641, People's Republic of China (hust.wuwen@gmail.com)
*: *Corresponding author.

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Abstract

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Abstract

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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.