Baker's Theorem on Linear Forms in Logarithms and Applications

Abstract

In 1966, Baker proved some considerable results about linear forms in the logarithms of algebraic numbers. In the first part of this thesis, we present the Schneider-Lang theorem in one dimension and some of its consequences. In the second part, we present the Schneider-Lang theorem in higher dimension and some of its corollaries. Such corollaries will be used later to prove some versions of Baker’s Theorem. Some consequences and applications of Baker’s Theorem have been presented at the end of the dissertation.