manuscripta mathematica

, Volume 22, Issue 1, pp 87–103 | Cite as

Reelle algebraische Funktionen mit vorgegebenen Null- und Polstellen

  • Wulf-Dieter Geyer


This note continues the investigations of Knebusch on algebraic curves over real closed fields and was initiated by reading [3]. Especially we ask for the existence of real algebraic functions with given zeroes and poles, a question going back to Witt [4]. We study the real nature of coverings of real algebraic curves, and if the covering has degree two, we get algebraic proofs for results, which in the classical case have been obtained by topological methods in [2].


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  1. [1]
    GEYER, W.-D.: Dualität bei abelschen Varietäten über reell abgeschlossenen Körpern, J. reine angew. Math. (1977)Google Scholar
  2. [2]
    GEYER, W.-D. & MARTENS, G.: Überlagerungen berandeter Kleinscher Flächen, Math. Ann.228, 101–111 (1977)Google Scholar
  3. [3]
    KNEBUSCH, M.: On Algebraic Curves over Real Closed Fields. I, II, Math. Z.150, 49–70;151, 189–205 (1976)Google Scholar
  4. [4]
    WITT, E.: Zerlegung reeller algebraischer Funktionen in Quadrate. Schiefkörper über reellem Funktionenkörper, J. reine angew. Math.171, 4–11 (1939)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Wulf-Dieter Geyer
    • 1
  1. 1.Mathematisches Institut der Universität Erlangen-NürnbergErlangenW.-Germany

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