Antisymmetric Paramodular Forms of Weights 2 and 3
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Antisymmetric Paramodular Forms of Weights 2 and 3
Author(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]
Journal title :
International Mathematics Research Notices
Pages :
6926-6946
Publisher :
Oxford University Press (OUP)
Publication date :
2020-10-23
ISSN :
1073-7928
HAL domain(s) :
Mathématiques [math]
English abstract : [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 ...
Show more >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 $\mathbb{Q}$.Show less >
Show more >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 $\mathbb{Q}$.Show less >
Language :
Anglais
Popular science :
Non
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