Statistics for ordinary Artin-Schreier covers and other p-rank strata

2013/04/30 by Alina Bucur, Chantal David, Bucur, Alina +5
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1304.7876

Abstract

We study the distribution of the number of points and of the zeroes of the zeta function in different p-rank strata of Artin-Schreier covers over \F_q when q is fixed and the genus goes to infinity. The p-rank strata considered include the ordinary family, the whole family, and the family of curves with p-rank equal to p-1. While the zeta zeroes always approach the standard Gaussian distribution, the number of points over \F_q has a distribution that varies with the specific family.

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