Linear independence of logarithms of Algebraic Numbers[MatSciRep: 116]

Abstract

The aim of the first part of these lectures (Chapters 2 to 6) is to give a complete proof of Baker's Theorem. In the second part of these lectures, which starts with the seventh Chapter, produces explicit measures of linear independence of logarithms of algebraic numbers. In this Chapter the author proves such an estimate by using the method of the first part. The aim is to present a proof as transparent as possible, not to give a sharp estimate. The result we reach is far from the best known, but is non trivial, and is quite sufficient for many Diophantine problems. Refinements of this estimate will be discussed in Chapter 10.