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Eisenstein Series

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

Abstract

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 \(\varepsilon_k(\Gamma)\).

Keywords

Zeta Function Modular Form Theta Function Fourier Expansion Eisenstein Series 
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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