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arXiv · 2602.19781

Explicit formulas and exact values for the number of rational points on singular curves over finite fields

Lorenzo Beninati
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Abstract

We provide new explicit formulas for bounding the number of rational points on singular curves over finite fields. This enables us to obtain exact values of N q (g, $\pi$) which is defined as the maximum number of rational points over F q on a curve of geometric genus g and arithmetic genus $\pi$. We also give special attention to the case g = 2 in order to extend the work of Aubry and Iezzi on N q (0, $\pi$) and N q (1, $\pi$).

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Lorenzo Beninati. 2026-02-23. Explicit formulas and exact values for the number of rational points on singular curves over finite fields. https://arxiv.org/abs/2602.19781

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