$S$-unit equation in two variables and Padé approximations

Abstract

In this article, we use Padé 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 Padé approximants with a simple argument relying on Mahler measure and on the local height, we refine the bound due to J.-H. Evertse.

13 pages

References in corpus (1)

• Padé approximation for a class of hypergeometric functions and parametric geometry of numbers