Congruence Between a Siegel and an Elliptic Modular Form

  • Günter Harder
Part of the Universitext book series (UTX)


The winter semester 2002/2003 was the last semester before my retirement from the university. It also happened that I was the chairman of the Colloquium and the speaker foreseen for February 7 had to cancel his visit. At about the same time I found some numerical support for a very general conjecture relating divisibilities of certain special values of L-functions to congruences between modular forms. I have been thinking about this kind of relationship for many years, but I never had any idea how one could find experimental evidence. But in the early 2003 C. Faber and G. van der Geer had written a program that produced lists of eigenvalues of Hecke operators on some special Siegel modular forms. After a few days of suspense we could compare their list with my list of eigenvalues of elliptic modular forms and verify the congruence in our examples.


Line Bundle Modular Form Cohomology Group Eisenstein Series Cusp Form 
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  1. [Fa-vdG]
    Faber, Carel; van der Geer, Gerard: Sur la cohomologie des systèmes locaux sur les espaces de modules des courbes de genre 2 et des surfaces abéliennes.I, C. R. Math. Acad. Sci. Paris 338 (2004), no. 5, 381–384. II, no. 6, 467–470zbMATHMathSciNetGoogle Scholar
  2. [Ha-Eis]
    G. Harder, Eisensteinkohomologie und die Konstruktion gemischter Motive, SLN 1562 The following two manuscripts on mixed motives and modular symbols can be found on my home page in my ftp-directory folder Eisenstein.Google Scholar
  3. [Mixmot]
    Modular construction of mixed motives IIGoogle Scholar
  4. [Modsym]
    Modular Symbols and Special Values of Automorphic L-FunctionsGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Günter Harder
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonnGermany

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