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arXiv · 1510.05601

Distributions of traces of Frobenius for smooth plane curves over finite fields

Reynald Lercier·Christophe Ritzenthaler·Florent Rovetta·Jeroen Sijsling·Benjamin Smith
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Abstract

In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperelliptic genus $3$ curves over small finite fields. In the present one, we give a heuristic explanation of these data, by extrapolating from results on the distribution of traces of Frobenius for plane curves whose degree is small with respect to the cardinality of their finite base field. In particular, our methods shed some new light on the asymmetry of the distribution around its mean value, which is related to the Serre obstruction.

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Reynald Lercier, Christophe Ritzenthaler, Florent Rovetta, Jeroen Sijsling, Benjamin Smith. 2015-10-19. Distributions of traces of Frobenius for smooth plane curves over finite fields. https://doi.org/10.1080/10586458.2017.1328321

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