Abstract
In Chap. 4 we deduced Baker’s Theorems 1.5 and 1.6 from Schneider-Lang’s Criterion. The proof used an extension of Gel’fond’s method in several variables. In Chapters 6 and 7, we extended Schneider’s method in several variables in order to prove the homogeneous transcendence result (Theorem 1.5) as well as quantitative refinements. The proofs did not involve any derivative at all. In Chap. 9, a single derivative was introduced, so that a second proof of Theorem 1.6 could be achieved, and at the same time measures for nonhomogeneous linear independence of logarithms could be derived. As we saw, it turned out that this approach was useful also for getting sharper estimates for homogeneous measures of linear independence.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Waldschmidt, M. (2000). On Baker’s Method. In: Diophantine Approximation on Linear Algebraic Groups. Grundlehren der mathematischen Wissenschaften, vol 326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11569-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-662-11569-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08608-3
Online ISBN: 978-3-662-11569-5
eBook Packages: Springer Book Archive