On Baker’s Method

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 326)


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.


Algebraic Group Auxiliary Function Algebraic Number Linear Independence Rational Integer 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Pierre et Marie Curie (Paris VI)Paris Cedex 05France

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