Surjectivity of Siegel Φ-operator for square free level and small weight
Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 121-144.

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.

Nous démontrons la surjectivité de l’opérateur Φ de Siegel pour des formes modulaires pour certains groupes de congruence de Sp(2,) et de poids 4, où les techniques standards (séries de Poincaré ou séries de Klingen-Eisenstein) ne marchent pas. Nous utilisons des séries thêta et le problème de base pour plusieurs genres.

DOI: 10.5802/aif.2702
Classification: 11F46, 11F27
Keywords: Siegel modular form, $\Phi $-operator, Theta series
Mot clés : formes modulaires de Siegel, l’opérateur $\Phi $, séries de thêta
Böcherer, Siegfried 1; Ibukiyama, Tomoyoshi 2

1 Kunzenhof 4B 79117 Freiburg (Germany)
2 Osaka University Graduate School of Science Department of Mathematics Machikaneyama 1-1, Toyonaka Osaka, 560-0043 (Japan)
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Böcherer, Siegfried; Ibukiyama, Tomoyoshi. Surjectivity of Siegel $\Phi $-operator for square free level and small weight. Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 121-144. doi : 10.5802/aif.2702. http://www.numdam.org/articles/10.5802/aif.2702/

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