$S$-unit equation in two variables and Padé approximations
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866910492521398272 |
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| author | Hirata-Kohno, Noriko Kawashima, Makoto Poëls, Anthony Washio, Yukiko |
| author_facet | Hirata-Kohno, Noriko Kawashima, Makoto Poëls, Anthony Washio, Yukiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14399 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $S$-unit equation in two variables and Padé approximations Hirata-Kohno, Noriko Kawashima, Makoto Poëls, Anthony Washio, Yukiko Number Theory 11D45 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. |
| title | $S$-unit equation in two variables and Padé approximations |
| topic | Number Theory 11D45 |
| url | https://arxiv.org/abs/2211.14399 |