Congruences for Siegel modular forms

[Congruences pour les formes modulaires de Siegel]

Choi, Dohoon ; Choie, YoungJu ; Richter, Olav K.

Annales de l'Institut Fourier, Tome 61 (2011), p. 1455-1466 / Harvested from Numdam

Résumé

Nous utilisons des résultats récents sur les formes de Jacobi pour étudier des congruences et des filtrations des formes modulaires de Siegel de degré $2$. En particulier, nous déterminons quand un analogue de l’opérateur $U(p)$ d’Atkin appliqué à une forme modulaire de Siegel du degré $2$ est non nul modulo un nombre premier $p$. Nous donnons des exemples explicites pour illustrer ces résultats.

Abstract

We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree $2$. In particular, we determine when an analog of Atkin’s $U(p)$-operator applied to a Siegel modular form of degree $2$ is nonzero modulo a prime $p$. Furthermore, we discuss explicit examples to illustrate our results.

Détail

Publié le : 2011-01-01

MR 2951499 | Zbl 1264.11036

DOI : https://doi.org/10.5802/aif.2646
Classification:  11F33,  11F46,  11F50
Mots clés: congruences, formes modulaires de Siegel

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