Plane Curves

  • Michael D. Fried
  • Moshe Jarden
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 11)


Here (Corollary 4.8) we use Theorem 3.14 to prove the following: If f (X,Y) is an absolutely irreducible polynomial of degree d defined over a field K of q elements,then the number N of K-rational solutions to the equation f (X, Y)= 0 \(\left| {N - (q - 1)} \right|(d - 1)(d - 2)\sqrt q + d.\)


Prime Ideal Local Ring Prime Divisor Plane Curve Irreducible Polynomial 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Michael D. Fried
    • 1
  • Moshe Jarden
    • 2
  1. 1.Mathematical DepartmentUniversity of FloridaGainsvilleUSA
  2. 2.School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityRamat Aviv, Tel AvivIsrael

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