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arXiv · 2602.01820

Quantitativity on the number of rational points in the Mordell conjecture

Jiawei Yu·Xinyi Yuan·Shengxuan Zhou
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Abstract

In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mordell conjecture proposed by Mazur and proved by Vojta, Dimitrov-Gao-Habegger, and K\"uhne. The main body of this paper consists of two parts: Part I for arithmetic estimates and Part II for analytic estimates.

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Jiawei Yu, Xinyi Yuan, Shengxuan Zhou. 2026-02-02. Quantitativity on the number of rational points in the Mordell conjecture. https://arxiv.org/abs/2602.01820

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