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

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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https://hal.inria.fr/hal-01217995
Contributor : Benjamin Smith <>
Submitted on : Tuesday, October 20, 2015 - 2:16:01 PM
Last modification on : Wednesday, July 15, 2020 - 2:03:08 PM

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Reynald Lercier, Christophe Ritzenthaler, Florent Rovetta, Jeroen Sijsling, Benjamin Smith. Distributions of traces of Frobenius for smooth plane curves over finite fields. Experimental Mathematics, Taylor & Francis, 2019, 28 (1), pp.39-48. ⟨10.1080/10586458.2017.1328321⟩. ⟨hal-01217995⟩

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