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

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

10 Downloads (Pure)

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

Access to Document

10.1016/j.jnt.2010.05.009

planecurves.pdfOther version, 211 KB

Cite this

@article{127f74bb06a14c3c84cfe6c516a73934,

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)",

author = "Alina Bucur and Chantal David and Brooke Feigon and Matilde Lal{\'i}n",

year = "2010",

month = nov,

doi = "10.1016/j.jnt.2010.05.009",

language = "English",

volume = "130",

pages = "2528--2541",

journal = "Journal of Number Theory",

publisher = "Academic Press Inc.",

number = "11",

}

TY - JOUR

T1 - Fluctuations in the number of points on smooth plane curves over finite fields

AU - Bucur, Alina

AU - David, Chantal

AU - Feigon, Brooke

AU - Lalín, Matilde

PY - 2010/11

Y1 - 2010/11

N2 - 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)

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)

U2 - 10.1016/j.jnt.2010.05.009

DO - 10.1016/j.jnt.2010.05.009

M3 - Article

VL - 130

SP - 2528

EP - 2541

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 11

ER -