Geodesic
The Thue--Mahler equation in a~relative field and approximation of algebraic numbers by algebraic numbers
Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 677-707

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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. 
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     author = {S. V. Kotov and V. G. Sprindzhuk},
     title = {The {Thue--Mahler} equation in a~relative field and approximation of algebraic numbers by algebraic numbers},
     journal = {Izvestiya. Mathematics },
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     volume = {11},
     number = {4},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a0/}
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S. V. Kotov; V. G. Sprindzhuk. The Thue--Mahler equation in a~relative field and approximation of algebraic numbers by algebraic numbers. Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 677-707. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a0/