$S$-unit equation in two variables and Pad\'{e} approximations
Number Theory
2024-06-19 v1
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 -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.
Keywords
Cite
@article{arxiv.2211.14399,
title = {$S$-unit equation in two variables and Pad\'{e} approximations},
author = {Noriko Hirata-Kohno and Makoto Kawashima and Anthony Poëls and Yukiko Washio},
journal= {arXiv preprint arXiv:2211.14399},
year = {2024}
}
Comments
13 pages