Advertisement

Elliptic Curves and Modular Forms

  • Haruzo Hida
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

We now describe basics of elliptic curves and modular curves in three steps:
  1. 1.

    as plane curves over a field;

     
  2. 2.

    as scheme/group functor over a ring;

     
  3. 3.

    modular forms as functorial rules on modular curves.

     

Keywords

Prime Ideal Modular Form Elliptic Curve Local Ring Elliptic Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [ALG]
    R. Hartshorne, Algebraic Geometry. Graduate Texts in Mathematics, vol. 52 (Springer-Verlag, New York, 1977)Google Scholar
  2. [CRT]
    H. Matsumura, Commutative Ring Theory. Cambridge Studies in Advanced Mathematics, vol. 8 (Cambridge University Press, New York, 1986)Google Scholar
  3. [DAV]
    G. Faltings, C.-L. Chai, Degeneration of Abelian Varieties (Springer-Verlag, New York, 1990)Google Scholar
  4. [EEK]
    A. Weil, Elliptic Functions According to Eisenstein and Kronecker (Springer-Verlag, Heidelberg, 1976)Google Scholar
  5. [GME]
    H. Hida, Geometric Modular Forms and Elliptic Curves, 2nd edn. (World Scientific, Singapore, 2011)Google Scholar
  6. [IAT]
    G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions (Princeton University Press, Princeton, NJ, 1971)Google Scholar
  7. [LFE]
    H. Hida, Elementary Theory of L-Functions and Eisenstein Series. London Mathematical Society Student Texts, vol. 26 (Cambridge University Press, Cambridge, 1993)Google Scholar
  8. [REC]
    J. Silverman, J. Tate, Rational Points on Elliptic Curves. Undergraduate Texts in Mathematics (Springer-Verlag, New York, 1992)Google Scholar
  9. [T3]
    J. Tate, A review of non-Archimedean elliptic functions, in Elliptic Curves, Modular Forms, & Fermat’s Last Theorem. Series in Number Theory I (International Press, Boston, 1995), pp. 162–184Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Haruzo Hida
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations