Linear Forms in the Logarithms of Algebraic Numbers Close to 1 and Applications to Diophantine Equations

摘要

In 1974, Shorey established the first sharp lower bound for linear forms in the logarithms of real algebraic numbers close to 1. His estimate was subsequently slightly refined and applied to various Diophantine equations. In many cases, it yields very spectacular statements. We survey several of its applications and we discuss some new ones.