Multiplicative dependence of rational values modulo approximate finitely generated groups
Fuente:
arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917847983194112 |
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| author | Bérczes, Attila Bugeaud, Yann Győry, Kálmán Mello, Jorge Ostafe, Alina Sha, Min |
| author_facet | Bérczes, Attila Bugeaud, Yann Győry, Kálmán Mello, Jorge Ostafe, Alina Sha, Min |
| contents | In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are `close' (with respect to the Weil height) to division groups of finitely generated multiplicative groups of a number field $K$. For example, we show that under some conditions on rational functions $f_1, \ldots, f_n\in K(X)$, there are only finitely many elements $α\in K$ such that $f_1(α),\ldots,f_n(α)$ are multiplicatively dependent modulo such sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_05371 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Multiplicative dependence of rational values modulo approximate finitely generated groups Bérczes, Attila Bugeaud, Yann Győry, Kálmán Mello, Jorge Ostafe, Alina Sha, Min Number Theory In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are `close' (with respect to the Weil height) to division groups of finitely generated multiplicative groups of a number field $K$. For example, we show that under some conditions on rational functions $f_1, \ldots, f_n\in K(X)$, there are only finitely many elements $α\in K$ such that $f_1(α),\ldots,f_n(α)$ are multiplicatively dependent modulo such sets. |
| title | Multiplicative dependence of rational values modulo approximate finitely generated groups |
| topic | Number Theory |
| url | https://arxiv.org/abs/2107.05371 |