On the quantitative subspace theorem

In this survey, we give an overview of recent improvements upon the Quantitative Subspace Theorem, obtained jointly with R. Ferretti, which follow from work in [9]. Further, we give a new gap principle with which we can estimate the number of subspaces containing the “small solutions” of the systems of inequalities under consideration. As an introduction, we start with a quantitative version of Roth's theorem. Bibl. 28 titles.