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Results in Mathematics

, Volume 44, Issue 3–4, pp 362–374 | Cite as

Some Properties of Reduced Drinfeld Modular Polynomials

  • Gerhard Rosenberger
  • Xueli Wang
Article
  • 27 Downloads

Abstract

In this paper we introduce a new kind of modular polynomials for rank 2 Drinfeld modules and discuss some properties of them.

Keywords

Drinfeld modular polynomials 

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References

  1. [Bae]
    Sunghan Bae, On the modular equation for Drinfeld modules of rank 2, J. of Number theory. 42 (1992), 123–133MathSciNetzbMATHCrossRefGoogle Scholar
  2. [Cohen]
    Paula Cohen, On the coefficients of the transformation polynomials for the elliptic modular function, Math. Proc. Camb. Phil. Soc. 95 (1984), 389–402zbMATHCrossRefGoogle Scholar
  3. [Gekeler 8.6.]
    Ernst-Ulrich Gekeler, Drinfeld modular curves, LNM., vol.1231, Springer, Berlin, Heidelberg, New York, 1986Google Scholar
  4. [Gekeler 8.8.]
    Ernst-Ulrich Gekeler, On the coefficients of Drinfeld modular forms, Invent. Math. 93 (1988), 667–700MathSciNetzbMATHCrossRefGoogle Scholar
  5. [Gekeler 9.7.]
    Ernst-Ulrich Gekeler, On the Drinfeld discriminant function, Composito Math. 106 (1997), 181–202MathSciNetzbMATHCrossRefGoogle Scholar
  6. [Hsia]
    Liang-Chung Hsia, On the coefficients of modular polynomials for Drinfeld modules, J. of Number theory. 72 (1998), 236–256MathSciNetzbMATHCrossRefGoogle Scholar
  7. [Mueller]
    V. Müller, Ein Algorithmus zur Bestimmung der Punktanzahl elliptischer Kurven über endlichen Körpern der Charakteristik grösser drei. Dissertation, Technischen Fakultät der Universität des Saarlandes, 1995Google Scholar
  8. [Schoof]
    R. Schoof, Counting points of elliptic curves over finite fields, J.Th. des. Nombres Bordeaux(Serie 2) 7 (1995), 219–254MathSciNetzbMATHCrossRefGoogle Scholar
  9. [Silverman]
    J.H. Silverman, Arithmetic of elliptic curves, Graduate text in Mathematics, Springer-Verlag, New York, 1986.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.Department of MathematicsDortmund UniversityDortmundGermany
  2. 2.Department of MathematicsHunan UniversityChangshaP.R.China
  3. 3.Department of MathematicsGuangzhou UniversityGuangzhouP.R.China
  4. 4.State key Lab. of Information SecurityBeijing

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