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arXiv · 2411.13522

Heights and morphisms in number fields

Matt Olechnowicz
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Abstract

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.

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Matt Olechnowicz. 2024-11-20. Heights and morphisms in number fields. https://arxiv.org/abs/2411.13522

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