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, Volume 72, Issue 1, pp 67–79 | Cite as

Elementary Abelianp-extensions of algebraic function fields

  • Arnaldo Garcia
  • Henning Stichtenoth


LetK be a field of characteristicp>0 andF/K be an algebraic function field. We obtain several results on Galois extensionsE/F with an elementary Abelian Galois group of orderp n.
  1. (a)

    E can be generated overF by some elementy whose minimal polynomial has the specific formT pnTz.

  2. (b)

    A formula for the genus ofE is given.

  3. (c)

    IfK is finite, then the genus ofE grows much faster than the number of rational points (as [EF] → ∞).

  4. (d)

    We present a new example of a function fieldE/K whose gap numbers are nonclassical.



Function Field Algebraic Curf Minimal Polynomial Galois Extension Constant Field 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Arnaldo Garcia
    • 1
  • Henning Stichtenoth
    • 2
  1. 1.Pura e AplicadaInstituto de MatematicaRio de JaneiroBrazil
  2. 2.Fachbereich 6-MathematikUniversität GHS EssenEssen 1Fed. Rep. Germany

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