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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.06665 |
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Table of 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.