S-unit equation in two variables and Padé approximations
Résumé
In this paper, we use Padé approximations, constructed by the second and third author for binomial functions, to give a new upper bound for the number of the solutions of the $S$-unit equation in two variables. Combining explicit Padé approximants with a simple argument relying on Mahler measure as well as the local height, we refine the bound due to Evertse.
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