A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen[1]

  • [1] California Institute of Technology Department of Mathematics 253-37 Caltech, Pasadena, CA 91125 (USA)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 6, page 1735-1766
  • ISSN: 0373-0956

Abstract

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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F . We do this for automorphic representations of an arbitrary reductive group G over F , which is compact at infinity. In the special case where G is an inner form of GSp ( 4 ) over ℚ , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

How to cite

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Mazanti Sorensen, Claus. "A generalization of level-raising congruences for algebraic modular forms." Annales de l’institut Fourier 56.6 (2006): 1735-1766. <http://eudml.org/doc/10190>.

@article{MazantiSorensen2006,
abstract = {In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field $F$. We do this for automorphic representations of an arbitrary reductive group $G$ over $F$, which is compact at infinity. In the special case where $G$ is an inner form of $\{\rm GSp\}(4)$ over $\mathbb\{Q\}$, we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.},
affiliation = {California Institute of Technology Department of Mathematics 253-37 Caltech, Pasadena, CA 91125 (USA)},
author = {Mazanti Sorensen, Claus},
journal = {Annales de l’institut Fourier},
keywords = {Level-raising; algebraic modular forms; level-raising},
language = {eng},
number = {6},
pages = {1735-1766},
publisher = {Association des Annales de l’institut Fourier},
title = {A generalization of level-raising congruences for algebraic modular forms},
url = {http://eudml.org/doc/10190},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Mazanti Sorensen, Claus
TI - A generalization of level-raising congruences for algebraic modular forms
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 6
SP - 1735
EP - 1766
AB - In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field $F$. We do this for automorphic representations of an arbitrary reductive group $G$ over $F$, which is compact at infinity. In the special case where $G$ is an inner form of ${\rm GSp}(4)$ over $\mathbb{Q}$, we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.
LA - eng
KW - Level-raising; algebraic modular forms; level-raising
UR - http://eudml.org/doc/10190
ER -

References

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