1987 | OriginalPaper | Buchkapitel
The Hecke-Eisenstein and Klein Forms
verfasst von : Serge Lang
Erschienen in: Introduction to Modular Forms
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.