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Fluctuations in the number of points on smooth plane curves over finite fields |
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| Authors: | Alina Bucur Chantal David Brooke Feigon |
| Affiliation: | a University of California at San Diego, United States b Institute for Advanced Study, United States c Concordia University, Canada d University of Toronto, Canada e University of Alberta, Canada |
| Abstract: | In this note, we study the fluctuations in the number of points on smooth projective plane curves over a finite field Fq 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 (2004) [8]. |
| Keywords: | Plane curves Finite fields Number of points |
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