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arXiv · 0912.4761

The fluctuations in the number of points of smooth plane curves over finite fields

Alina Bucur·Chantal David·Brooke Feigon·Matilde Lalín
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Abstract

In this note, we study the fluctuations in the number of points of smooth projective plane curves over finite fields $\mathbb{F}_q$ as $q$ is fixed and the genus varies. More precisely, we show that these fluctuations are predicted by a natural probabilistic model, in which the points of the projective plane impose independent conditions on the curve. The main tool we use is a geometric sieving process introduced by Poonen.

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Alina Bucur, Chantal David, Brooke Feigon, Matilde Lalín. 2009-12-24. The fluctuations in the number of points of smooth plane curves over finite fields. https://doi.org/10.1016/j.jnt.2010.05.009

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