Fluctuations in the number of points on smooth plane curves over finite fields

Alina Bucur; Chantal David; Brooke Feigon; Matilde Lalín

doi:10.1016/j.jnt.2010.05.009

Fluctuations in the number of points on smooth plane curves over finite fields

Alina Bucur, Chantal David, Brooke Feigon, Matilde Lalín

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19 Citations (Scopus)

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Abstract

In this note, we study the fluctuations in the number of points on smooth projective plane curves over a finite field 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)

Original language	English
Pages (from-to)	2528-2541
Number of pages	14
Journal	Journal of Number Theory
Volume	130
Issue number	11
DOIs	https://doi.org/10.1016/j.jnt.2010.05.009
Publication status	Published - Nov 2010

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10.1016/j.jnt.2010.05.009

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Cite this

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title = "Fluctuations in the number of points on smooth plane curves over finite fields",

abstract = "In this note, we study the fluctuations in the number of points on smooth projective plane curves over a finite field 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)",

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AU - Lalín, Matilde

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AB - In this note, we study the fluctuations in the number of points on smooth projective plane curves over a finite field 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)

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