The Hecke-Eisenstein and Klein Forms

  • Serge Lang
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 222)


We have seen in Chapter X, § 3 that the modular form G k has a q-expansion
$$ {G_k} = 2\zeta (k) + \cdots $$
So the value of the ordinary zeta function appears as the constant term of a modular form (Eisenstein series, as it is called). This phenomenon, first exploited by Klingen [Kl 3] and Siegel [Si 4], has been highly developed by Serre [Se 5] and others. We give here more examples.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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