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Artin–Schreier extensions of the rational function field

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Abstract

In this paper we study the arithmetic of Artin–Schreier extensions of \(\mathbb {F}_{q}(T)\). We determine the integral closure of \(\mathbb {F}_{q}[T]\) in Artin–Schreier extension of \(\mathbb {F}_{q}(T)\). We also investigate the average values of the \(L\)-functions of orders of Artin–Schreier extensions and study the average values of ideal class numbers when \(p=3\) in detail.

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Acknowledgments

The authors are enormously grateful to the referee whose comments and suggestions lead to a large improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, KAIST, Taejon, 305-701, Korea

    Sunghan Bae

  2. Department of Mathematics Education, Chungbuk National University, Cheongju, 361-763, Korea

    Hwanyup Jung

  3. Department of Mathematics, Chungnam National University, Daejon, 305-764, Korea

    Pyung-Lyun Kang

Authors
  1. Sunghan Bae
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  2. Hwanyup Jung
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  3. Pyung-Lyun Kang
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Corresponding author

Correspondence to Hwanyup Jung.

Additional information

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2013042157).

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Bae, S., Jung, H. & Kang, PL. Artin–Schreier extensions of the rational function field. Math. Z. 276, 613–633 (2014). https://doi.org/10.1007/s00209-013-1215-0

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