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Surjectivity of Siegel Φ -operator for square free level and small weight

Siegfried Böcherer, Tomoyoshi Ibukiyama (2012)

Annales de l’institut Fourier

We show the surjectivity of the (global) Siegel Φ -operator for modular forms for certain congruence subgroups of Sp ( 2 , ) and weight k = 4 , where the standard techniques (Poincaré series or Klingen-Eisenstein series) are no longer available. Our main tools are theta series and genus versions of basis problems.

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