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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.19781 |
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Table of Contents:
- 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, $π$) which is defined as the maximum number of rational points over F q on a curve of geometric genus g and arithmetic genus $π$. We also give special attention to the case g = 2 in order to extend the work of Aubry and Iezzi on N q (0, $π$) and N q (1, $π$).