Congruences for Siegel modular forms

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

doi:10.5802/aif.2646

Congruences for Siegel modular forms
[Congruences pour les formes modulaires de Siegel]

Choi, Dohoon ¹ ; Choie, YoungJu ² ; Richter, Olav K.³

¹ Korea Aerospace University School of Liberal Arts and Sciences Goyang 412-791 (South Korea)
² Pohang University of Science and Technology Department of Mathematics Pohang 790-784 (South Korea)
³ University of North Texas Department of Mathematics Denton, TX 76203 (USA)

Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1455-1466.

Résumé
Abstract

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.

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.

MR Zbl

DOI : 10.5802/aif.2646

Classification : 11F33, 11F46, 11F50
Keywords: Congruences, Siegel modular forms
Mot clés : congruences, formes modulaires de Siegel

Affiliations des auteurs :

Choi, Dohoon ¹ ; Choie, YoungJu ² ; Richter, Olav K. ³

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     title = {Congruences for {Siegel} modular forms},
     journal = {Annales de l'Institut Fourier},
     pages = {1455--1466},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
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     zbl = {1264.11036},
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Choi, Dohoon; Choie, YoungJu; Richter, Olav K. Congruences for Siegel modular forms. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1455-1466. doi : 10.5802/aif.2646. http://www.numdam.org/articles/10.5802/aif.2646/

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