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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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 languageEnglish
Pages (from-to)2528-2541
Number of pages14
JournalJournal of Number Theory
Volume130
Issue number11
DOIs
Publication statusPublished - Nov 2010

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