S-unit equation in two variables and Padé approximations - Archive ouverte HAL
Article Dans Une Revue International Journal of Number Theory Année : 2023

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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hal-04455067 , version 1 (13-02-2024)

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Noriko Hirata-Kohno, Makoto Kawashima, Anthony Poëls, Yukiko Washio. S-unit equation in two variables and Padé approximations. International Journal of Number Theory, 2023, 19 (10), pp.2427-2442. ⟨10.1142/S1793042123501191⟩. ⟨hal-04455067⟩
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