Cohen lifting of modular forms

  • Gérard Lion
  • Michèle Vergne
Part of the Progress in Mathematics book series (PM, volume 6)


Let K be a real quadratic field. We have discussed in 2.8 the kernel Ω(τ, z1,z2) of the Doi-Naganuma correspondence constructed by Zagier. We will modify this construction in order to obtain the correspondence, conjectured by H. Cohen ([5]), between modular forms in one variable with respect to any congruence subgroup Γ0(N) and Hilbert modular forms in two variables. We consider \(K = Q\left( {\sqrt D } \right)\), with D ≡ 1 mod 4 and we keep the notations of Section 2.8.


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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gérard Lion
    • 1
  • Michèle Vergne
    • 2
  1. 1.X U.E.R. de Sciences EconomiquesUniversité de ParisNanterreFrance
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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