$S$-integral preperiodic points for monomial semigroups over number fields
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910338987851776 |
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| author | Young, Marley |
| author_facet | Young, Marley |
| contents | We consider semigroup dynamical systems defined by several monnomials over a number field $K$. We prove a finiteness result for preperiodic points of such systems which are $S$-integral with respect to a non-preperiodic point $β$, which is uniform as $β$ varies over number fields of bounded degree. This generalises results of Baker, Ih and Rumely, which were made uniform by Yap, and verifies a special case of a natural generalisation of a conjecture of Ih. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $S$-integral preperiodic points for monomial semigroups over number fields Young, Marley Number Theory Dynamical Systems 37P05, 11G50, 11J86 We consider semigroup dynamical systems defined by several monnomials over a number field $K$. We prove a finiteness result for preperiodic points of such systems which are $S$-integral with respect to a non-preperiodic point $β$, which is uniform as $β$ varies over number fields of bounded degree. This generalises results of Baker, Ih and Rumely, which were made uniform by Yap, and verifies a special case of a natural generalisation of a conjecture of Ih. |
| title | $S$-integral preperiodic points for monomial semigroups over number fields |
| topic | Number Theory Dynamical Systems 37P05, 11G50, 11J86 |
| url | https://arxiv.org/abs/2402.13713 |