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The Eichler–Shimura Relation and L-functions

  • Fred Diamond
  • Jerry Shurman
Part of the Graduate Texts in Mathematics book series (GTM, volume 228)

Abstract

This chapter arrives at the first version of the Modularity Theorem stated in the preface to the book: For any elliptic curve E over \(\mathbb{Q}\) there exists a weight 2 newform f such that the Fourier coefficients \(a_p(f)\) are equal to the solution-counts \(a_p(\textit{E})\) of a Weierstrass equation for E modulo p.

Keywords

Modulus Space Prime Ideal Elliptic Curve Maximal Ideal 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.

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Copyright information

© Springer Science+Business Media New York 2005

Authors and Affiliations

  • Fred Diamond
    • 1
  • Jerry Shurman
    • 2
  1. 1.Department of MathematicsKing’s College London StrandLondonUK
  2. 2.Department of MathematicsReed CollegePortlandUSA

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