Statistics for ordinary Artin-Schreier covers and other $p$-rank strata
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- by Alina Bucur, Chantal David, Brooke Feigon and Matilde Lalín PDF
- Trans. Amer. Math. Soc. 368 (2016), 2371-2413 Request permission
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 $\mathbb {F}_q$ 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 covers with $p$-rank equal to $p-1.$ While the zeta zeroes always approach the standard Gaussian distribution, the number of points over $\mathbb {F}_q$ has a distribution that varies with the specific family.References
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Additional Information
- Alina Bucur
- Affiliation: Department of Mathematics, University of California at San Diego, 9500 Gilman Drive $\#$0112, La Jolla, California 92093
- MR Author ID: 751232
- Email: alina@math.ucsd.edu
- Chantal David
- Affiliation: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve West, Montreal, QC H3G 1M8, Canada
- MR Author ID: 363267
- Email: cdavid@mathstat.concordia.ca
- Brooke Feigon
- Affiliation: Department of Mathematics, The City College of New York, CUNY, NAC 8/133, New York, New York 10031
- Email: bfeigon@ccny.cuny.edu
- Matilde Lalín
- Affiliation: Département de Mathématiques et de Statistique, Université de Montréal, CP 6128, succ. Centre-ville, Montreal, QC H3C 3J7, Canada
- Email: mlalin@dms.umontreal.ca
- Received by editor(s): May 5, 2013
- Received by editor(s) in revised form: January 13, 2014
- Published electronically: July 10, 2015
- Additional Notes: The first author was supported by the Simons Foundation #244988 and the UCSD Hellman Fellows Program (2012–2013 Hellman Fellowship)
The second and fourth authors were supported by the Natural Sciences and Engineering Research Council of Canada (Discovery Grant 155635-2008 to the second author, 355412-2008 to the fourth author), and by the Fonds de recherche du Québec - Nature et technologies (144987 to the fourth author, 166534 to the second and fourth authors)
The third author was supported by the National Science Foundation (DMS-1201446) and PSC-CUNY - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 2371-2413
- MSC (2010): Primary 11G20; Secondary 11M50, 14G15
- DOI: https://doi.org/10.1090/tran/6410
- MathSciNet review: 3449243