The Eichler–Shimura Relation and L-functions

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


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.


Modulus Space Prime Ideal Elliptic Curve Maximal Ideal Elliptic Curf 
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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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