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

DOI10.1016/j.jnt.2010.05.009zbMath1210.11070arXiv0912.4761OpenAlexW1997446756MaRDI QIDQ710489

Brooke Feigon, Alina Bucur, Chantal David, Matilde N. Lalín

Publication date: 19 October 2010

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.4761

zbMATH Keywords

finite fieldsplane curvesnumber of points

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99)

Related Items (13)

Random hypersurfaces and embedding curves in surfaces over finite fields ⋮ On the distribution of zeroes of Artin-Schreier \(L\)-functions ⋮ On the distribution of the number of points on a family of curves over finite fields ⋮ Motivic random variables and representation stability. II: Hypersurface sections ⋮ A heuristic for the distribution of point counts for random curves over a finite field ⋮ The probability that a complete intersection is smooth ⋮ Most plane curves over finite fields are not blocking ⋮ ON THE DISTRIBUTION OF THE RATIONAL POINTS ON CYCLIC COVERS IN THE ABSENCE OF ROOTS OF UNITY ⋮ Distribution of zeta zeroes for abelian covers of algebraic curves over a finite field ⋮ Semiample Bertini theorems over finite fields ⋮ Distributions of Traces of Frobenius for Smooth Plane Curves Over Finite Fields ⋮ The distribution of points on superelliptic curves over finite fields ⋮ Statistics for ordinary Artin-Schreier covers and other $p$-rank strata

Cites Work

• The fluctuations in the number of points on a hyperelliptic curve over a finite field
• Bertini theorems over finite fields
• Statistics for Traces of Cyclic Trigonal Curves over Finite Fields
• Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess
• More points than expected on curves over finite field extensions
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