Rational points of bounded height on entire curves
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913785808158720 |
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| author | Gasbarri, Carlo |
| author_facet | Gasbarri, Carlo |
| contents | Let $X$ be an affine or a projective variety defined over a number field $K$ and $φ:{\bf C}\to X({\bf C})$ be a holomorphic map with Zariski dense image. We estimate the number of rational points of height bounded by $H$ in the image of a disk of radius $r$ in terms of the the Nevanlinna characteristic function of $φ$ and $H$ in a way which generalize the classical Bombieri--Pila estimate to expanding domains. In general this bound is exponential but we show that for many values of $H$ and $r$, the bound is polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational points of bounded height on entire curves Gasbarri, Carlo Number Theory Algebraic Geometry 11G50, 11J37, 30D35 Let $X$ be an affine or a projective variety defined over a number field $K$ and $φ:{\bf C}\to X({\bf C})$ be a holomorphic map with Zariski dense image. We estimate the number of rational points of height bounded by $H$ in the image of a disk of radius $r$ in terms of the the Nevanlinna characteristic function of $φ$ and $H$ in a way which generalize the classical Bombieri--Pila estimate to expanding domains. In general this bound is exponential but we show that for many values of $H$ and $r$, the bound is polynomial. |
| title | Rational points of bounded height on entire curves |
| topic | Number Theory Algebraic Geometry 11G50, 11J37, 30D35 |
| url | https://arxiv.org/abs/2504.06665 |