Surjectivity of Siegel Φ-operator for square free level and small weight  [ Surjectivité de l’opérateur Φ de Siegel pour des niveaux sans facteur carré et pour petit poids ]
Annales de l'Institut Fourier, Tome 62 (2012) no. 1, p. 121-144
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.
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.
DOI : https://doi.org/10.5802/aif.2702
Classification:  11F46,  11F27
Mots clés: formes modulaires de Siegel, l’opérateur Φ, séries de thêta
@article{AIF_2012__62_1_121_0,
     author = {B\"ocherer, Siegfried and Ibukiyama, Tomoyoshi},
     title = {Surjectivity of Siegel $\Phi $-operator for square free level and small weight},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {1},
     year = {2012},
     pages = {121-144},
     doi = {10.5802/aif.2702},
     mrnumber = {2986268},
     zbl = {pre06064515},
     language = {en},
     url = {http://http://www.numdam.org/item/AIF_2012__62_1_121_0}
}
Böcherer, Siegfried; Ibukiyama, Tomoyoshi. Surjectivity of Siegel $\Phi $-operator for square free level and small weight. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 121-144. doi : 10.5802/aif.2702. http://www.numdam.org/item/AIF_2012__62_1_121_0/

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