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Zeta Functions of a Class of Artin–Schreier Curves with Many Automorphisms

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Directions in Number Theory

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 3))

Abstract

This paper describes a class of Artin–Schreier curves, generalizing results of Van der Geer and Van der Vlugt to odd characteristic. The automorphism group of these curves contains a large extraspecial group as a subgroup. Precise knowledge of this subgroup makes it possible to compute the zeta function of the curves in this class over the field of definition of all automorphisms in the subgroup.

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Acknowledgements

This research began at the Women in Numbers 3 workshop that took place April 20–25, 2014, at the Banff International Research Station (BIRS) in Banff, Alberta (Canada). We thank the organizers of this workshop as well as the hospitality of BIRS. We also thank Mike Zieve for pointing out some references to us.

IB is partially supported by DFG priority program SPP 1489, WH is partially supported by NSF grant DMS-1406066, and RS is supported by NSERC of Canada.

Author information

Authors and Affiliations

  1. Institute of Pure Mathematics, Ulm University, D-89069, Ulm, Germany

    Irene Bouw

  2. Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI, 48109, USA

    Wei Ho

  3. Department of Mathematics and Statistics, Villanova University, 800 Lancaster Avenue, Villanova, PA, 19085, USA

    Beth Malmskog

  4. Department of Mathematics and Statistics, University of Calgary, 2500 University, Drive NW, Calgary, AB, Canada, T2N 1N4

    Renate Scheidler

  5. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Padmavathi Srinivasan

  6. Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, VT, 05401, USA

    Christelle Vincent

Authors
  1. Irene Bouw
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  2. Wei Ho
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  3. Beth Malmskog
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  4. Renate Scheidler
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  5. Padmavathi Srinivasan
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  6. Christelle Vincent
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Corresponding author

Correspondence to Irene Bouw .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, Oregon, USA

    Ellen E. Eischen

  2. Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana, USA

    Ling Long

  3. Department of Mathematics, Colorado State University, Fort Collins, Colorado, USA

    Rachel Pries

  4. Department of Mathematics, University of Colorado, Boulder, Colorado, USA

    Katherine E. Stange

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© 2016 Springer International Publishing Switzerland

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Bouw, I., Ho, W., Malmskog, B., Scheidler, R., Srinivasan, P., Vincent, C. (2016). Zeta Functions of a Class of Artin–Schreier Curves with Many Automorphisms. In: Eischen, E., Long, L., Pries, R., Stange, K. (eds) Directions in Number Theory. Association for Women in Mathematics Series, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-30976-7_4

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