Antisymmetric Paramodular Forms of Weights 2 and 3
2019 ◽
Vol 2020
(20)
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pp. 6926-6946
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Keyword(s):
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 $\mathbb{Q}$.
2009 ◽
Vol 309
(16)
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pp. 5048-5059
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2006 ◽
Vol 128
(1)
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pp. 139-165
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2010 ◽
Vol 62
(2)
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pp. 456-472
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Keyword(s):
1952 ◽
Vol 48
(3)
◽
pp. 383-391
1979 ◽
Vol 35
(1)
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pp. 1-17
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