The Thue–Mahler equation in a relative field and approximation of algebraic numbers by algebraic numbers

A new estimate of the solutions of the generalized Thue–Mahler equation is derived, which explicitly exhibits the influence of all fundamental parameters of the equation on the magnitude of the solutions. Also, an effective power sharpening is given of “Liouville's inequality” relating to the approximation of algebraic numbers by algebraic numbers of a fixed field, which includes both Archimedean and non-Archimedean valuations.
Bibliography: 19 titles.