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

Siegfried Böcherer[1]; Tomoyoshi Ibukiyama[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)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 121-144
  • ISSN: 0373-0956

Abstract

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We show the surjectivity of the (global) Siegel Φ -operator for modular forms for certain congruence subgroups of Sp ( 2 , 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.

How to cite

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Böcherer, Siegfried, and Ibukiyama, Tomoyoshi. "Surjectivity of Siegel $\Phi $-operator for square free level and small weight." Annales de l’institut Fourier 62.1 (2012): 121-144. <http://eudml.org/doc/251070>.

@article{Böcherer2012,
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.},
affiliation = {Kunzenhof 4B 79117 Freiburg (Germany); Osaka University Graduate School of Science Department of Mathematics Machikaneyama 1-1, Toyonaka Osaka, 560-0043 (Japan)},
author = {Böcherer, Siegfried, Ibukiyama, Tomoyoshi},
journal = {Annales de l’institut Fourier},
keywords = {Siegel modular form; $\Phi $-operator; Theta series; Siegel modular forms; -operator; theta series},
language = {eng},
number = {1},
pages = {121-144},
publisher = {Association des Annales de l’institut Fourier},
title = {Surjectivity of Siegel $\Phi $-operator for square free level and small weight},
url = {http://eudml.org/doc/251070},
volume = {62},
year = {2012},
}

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
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 121
EP - 144
AB - 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.
LA - eng
KW - Siegel modular form; $\Phi $-operator; Theta series; Siegel modular forms; -operator; theta series
UR - http://eudml.org/doc/251070
ER -

References

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