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

@article{Bucur2013StatisticsFO,
  title={Statistics for ordinary Artin-Schreier covers and other -rank strata},
  author={Alina Bucur and Chantal David and Brooke Feigon and Matilde Lal{\'i}n},
  journal={Transactions of the American Mathematical Society},
  year={2013},
  volume={368},
  pages={2371-2413}
}
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 Fq 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 covers with p-rank equal to p − 1. While the zeta zeroes always approach the standard Gaussian distribution, the number of points over Fq has a distribution that varies with the specific family. 
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