S-unit equation in two variables and Pad\'e approximations
Abstract
In this article, we use Pad\'e approximations constructed for binomial functions, to give a new upper bound for the number of the solutions of the S-unit equation. Combining explicit formulae of these Pad\'e approximants with a simple argument relying on Mahler measure and on the local height, we refine the bound due to J.-H. Evertse.
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