Congruences for Siegel modular forms

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

doi:10.5802/aif.2646

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, Volume 61 (2011) no. 4, pp. 1455-1466.

Abstract
Résumé

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.

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.

MR Zbl

DOI: 10.5802/aif.2646

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

Author's affiliations:

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},
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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, Volume 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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