%0 Journal Article
%T Statistics for ordinary Artin-Schreier covers and other $p$-rank strata
%A Alina Bucur
%A Chantal David
%A Brooke Feigon
%A Matilde Lalin
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1304.7876v1