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Siegfried Böcherer; Tomoyoshi Ibukiyama
Surjectivity of Siegel $\Phi $-operator for square free level and small weight
(Surjectivité de l’opérateur $\Phi $ de Siegel pour des niveaux sans facteur carré et pour petit poids)
Annales de l'institut Fourier, 62 no. 1 (2012), p. 121-144, doi: 10.5802/aif.2702
Article PDF | Reviews MR 2986268 | Zbl pre06064515
Class. Math.: 11F46, 11F27
Keywords: Siegel modular form, $\Phi $-operator, Theta series

Résumé - Abstract

We show the surjectivity of the (global) Siegel $\Phi $-operator for modular forms for certain congruence subgroups of $\mathrm{Sp}(2,\mathbb{Z})$ 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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