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On linear independence measures of the values of Mahler functions

Published online by Cambridge University Press:  22 June 2018

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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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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018