[Surjectivité de l’opérateur de Siegel pour des niveaux sans facteur carré et pour petit poids]
Nous démontrons la surjectivité de l’opérateur de Siegel pour des formes modulaires pour certains groupes de congruence de 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 -operator for modular forms for certain congruence subgroups of and weight , 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.
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
@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},
pages = {121--144},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {62},
number = {1},
year = {2012},
doi = {10.5802/aif.2702},
mrnumber = {2986268},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2702/}
}
TY - JOUR AU - Böcherer, Siegfried AU - Ibukiyama, Tomoyoshi TI - Surjectivity of Siegel $\Phi $-operator for square free level and small weight JO - Annales de l'Institut Fourier PY - 2012 SP - 121 EP - 144 VL - 62 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2702/ DO - 10.5802/aif.2702 LA - en ID - AIF_2012__62_1_121_0 ER -
%0 Journal Article %A Böcherer, Siegfried %A Ibukiyama, Tomoyoshi %T Surjectivity of Siegel $\Phi $-operator for square free level and small weight %J Annales de l'Institut Fourier %D 2012 %P 121-144 %V 62 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2702/ %R 10.5802/aif.2702 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2702/
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