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
|Author:||Väänänen, Keijo1; Wu, Wen2|
1Department of Mathematical Science, University of Oulu
2School of Mathematics, South China University of Technology
|Online Access:||PDF Full Text (PDF, 0.2 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2018112749197
Cambridge University Press,
|Publish Date:|| 2018-12-22
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.
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
|Pages:||1297 - 1311|
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
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.
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.