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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: | open |
| Online Access: | PDF Full Text (PDF, 0.2 MB) |
| Persistent link: | http://urn.fi/urn:nbn:fi-fe2018112749197 |
| Language: | English |
| Published: |
Cambridge University Press,
2018
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| Publish Date: | 2018-12-22 |
| Description: |
AbstractWe 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. see all
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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. |