Heights and morphisms in number fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909397603581952 |
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| author | Olechnowicz, Matt |
| author_facet | Olechnowicz, Matt |
| contents | We give a formula with explicit error term for the number of $K$-rational points $P$ satisfying $H(f(P)) \le X$ as $X \to \infty$, where $f$ is a nonconstant morphism between projective spaces defined over a number field $K$ and $H$ is the absolute multiplicative Weil height. This yields formulae for the counting functions of $f(\mathbb{P}^m(K))$ with respect to the Weil height as well as of $\mathbb{P}^m(K)$ with respect to the Call-Silverman canonical height. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heights and morphisms in number fields Olechnowicz, Matt Number Theory Dynamical Systems We give a formula with explicit error term for the number of $K$-rational points $P$ satisfying $H(f(P)) \le X$ as $X \to \infty$, where $f$ is a nonconstant morphism between projective spaces defined over a number field $K$ and $H$ is the absolute multiplicative Weil height. This yields formulae for the counting functions of $f(\mathbb{P}^m(K))$ with respect to the Weil height as well as of $\mathbb{P}^m(K)$ with respect to the Call-Silverman canonical height. |
| title | Heights and morphisms in number fields |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2411.13522 |