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

DOI10.1090/TRAN/6410zbMATH Open1408.11062arXiv1304.7876OpenAlexW1889097938MaRDI QIDQ2787975

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Publication date: 7 March 2016

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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.

Full work available at URL: https://arxiv.org/abs/1304.7876

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