Families of automorphic forms

  • Roelof W. Bruggeman
Part of the Modern Birkhäuser Classics book series (MBC)


Up till now we have studied individual automorphic forms. These turn out to occur in families in a natural way. For instance, the Poincaré series depends continuously on the weight l, the unitary character x, and the spectral parameter s. The dependence on s is holomorphic. It is not clear from the series that there might be a holomorphic or meromorphic dependence on the character and the weight. In Chapters 9 and 10 we shall get meromorphy by functional analytic methods.


Parameter Space Open Subset Meromorphic Function Complex Manifold Cusp Form 
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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Roelof W. Bruggeman
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherland

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