On linear independence measures of the values of Mahler functions
Väänänen, Keijo; Wu, Wen (2018-06-22)
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
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.
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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