Eisenstein Series

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


For any congruence subgroup \(\Gamma\) of \(\mathrm{SL_2}(\mathbb{Z})\), the space \(\mathcal{M}_\textit{k}(\Gamma)\) of modular forms naturally decomposes into its subspace of cusp forms \(\mathcal{S}_\textit{k}(\Gamma)\) and the corresponding quotient space \(\mathcal{S}_\textit{k}(\Gamma)/\mathcal{S}_\textit{k}(\Gamma)\), the Eisenstein space \(\varepsilon_k(\Gamma)\).


Zeta Function Modular Form Theta Function Fourier Expansion Eisenstein Series 
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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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