Antisymmetric Paramodular Forms of Weights 2 and 3
Type de document :
Article dans une revue scientifique: Article original
DOI :
URL permanente :
Titre :
Antisymmetric Paramodular Forms of Weights 2 and 3
Auteur(s) :
Gritsenko, Valery [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Poor, Cris [Auteur]
Yuen, David [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Poor, Cris [Auteur]
Yuen, David [Auteur]
Titre de la revue :
International Mathematics Research Notices
Pagination :
6926-6946
Éditeur :
Oxford University Press (OUP)
Date de publication :
2020-10-23
ISSN :
1073-7928
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [en]
Abstract We define an algebraic set in $23$-dimensional projective space whose ${{\mathbb{Q}}}$-rational points correspond to meromorphic, antisymmetric, paramodular Borcherds products. We know two lines inside this algebraic ...
Lire la suite >Abstract We define an algebraic set in $23$-dimensional projective space whose ${{\mathbb{Q}}}$-rational points correspond to meromorphic, antisymmetric, paramodular Borcherds products. We know two lines inside this algebraic set. Some rational points on these lines give holomorphic Borcherds products and thus construct examples of Siegel modular forms on degree 2 paramodular groups. Weight $3$ examples provide antisymmetric canonical differential forms on Siegel modular three-folds. Weight $2$ is the minimal weight and these examples, via the paramodular conjecture, give evidence for the modularity of some rank 1 abelian surfaces defined over $\mathbb{Q}$.Lire moins >
Lire la suite >Abstract We define an algebraic set in $23$-dimensional projective space whose ${{\mathbb{Q}}}$-rational points correspond to meromorphic, antisymmetric, paramodular Borcherds products. We know two lines inside this algebraic set. Some rational points on these lines give holomorphic Borcherds products and thus construct examples of Siegel modular forms on degree 2 paramodular groups. Weight $3$ examples provide antisymmetric canonical differential forms on Siegel modular three-folds. Weight $2$ is the minimal weight and these examples, via the paramodular conjecture, give evidence for the modularity of some rank 1 abelian surfaces defined over $\mathbb{Q}$.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
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Source :
Date de dépôt :
2025-01-24T14:05:54Z
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