Effective bounds for solutions of \(S\)-unit equations and of Thue-Mahler equations
\textit{E. Bombieri} and \textit{P. B. Cohen} [Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4), 205-225 (1997; Zbl 0912.11028)] have developed a method in effective diophantine approximation, based on a reworked version of the Thue principle, the Dyson lemma and on the geometry of numbers. The present author sharpens the results of the above paper by reworking it and using, instead of the Thue principle, lower bounds of linear forms in two or three logarithms. As a result, he gives effective upper bounds for the size of solutions of \(S\)-unit equations and of Thue-Mahler equations. He also derives a new effective irrationality measure for algebraic numbers. Finally, he compares his estimates with analogous recent estimates of himself and \textit{K. Győry} [Acta Arith. 74, 67-80 (1996; Zbl 0861.11023) and 273-292 (1996; Zbl 0861.11024)].
effective irrationality measure for algebraic numbers
scientific article; zbMATH DE number 1236181