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arXiv · 1304.7876

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

Alina Bucur·Chantal David·Brooke Feigon·Matilde Lalin
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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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Alina Bucur, Chantal David, Brooke Feigon, Matilde Lalin. 2013-04-30. Statistics for ordinary Artin-Schreier covers and other $p$-rank strata. https://arxiv.org/abs/1304.7876

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