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hermite–padé approximation

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

On linear independence measures of the values of Mahler functions
Part of
- Diophantine approximation, transcendental number theory
Keijo Väänänen, Wen Wu
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 6 / December 2018

Published online by Cambridge University Press:

22 June 2018, pp. 1297-1311

Print publication:

December 2018
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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.