University of Oulu

Väänänen, K., Wu, W. (2018) On linear independence measures of the values of Mahler functions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 148 (06), 1297-1311. doi:10.1017/S0308210518000148

On linear independence measures of the values of Mahler functions

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Author: Väänänen, Keijo1; Wu, Wen2
Organizations: 1Department of Mathematical Science, University of Oulu
2School of Mathematics, South China University of Technology
Format: article
Version: accepted version
Access: embargoed
Persistent link: http://urn.fi/urn:nbn:fi-fe2018112749197
Language: English
Published: Cambridge University Press, 2018
Publish Date: 2018-12-22
Description:

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.

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Series: Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
ISSN: 0308-2105
ISSN-E: 1473-7124
ISSN-L: 0308-2105
Volume: 148
Issue: 6
Pages: 1297 - 1311
DOI: 10.1017/S0308210518000148
OADOI: https://oadoi.org/10.1017/S0308210518000148
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
Funding: The research of W.W. was supported by the Natural Science Foundation of China (Grant no. 11401188) and by the Academy of Finland’s Centre of Excellence in Analysis and Dynamics Research.
Copyright information: This article has been published in a revised form in Proceedings of the Royal Society of Edinburgh: Section A Mathematics, https://doi.org/10.1017/S0308210518000148. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © The Royal Society of Edinburgh.