Geodesic
Antisymmetric paramodular forms of weight~3
Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1702-1723

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The problem of the construction of antisymmetric paramodular forms of canonical weight 3 has been open since 1996. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer surfaces associated to $(1,t)$-polarised abelian surfaces. In this paper, we construct the first infinite family of antisymmetric paramodular forms of weight $3$ as automorphic Borcherds products whose first Fourier-Jacobi coefficient is a theta block. Bibliography: 32 titles.
Keywords: Siegel modular forms, automorphic Borcherds products, theta functions and Jacobi forms, moduli space of abelian and Kummer surfaces, affine Lie algebras and hyperbolic Lie algebras. 
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     author = {V. A. Gritsenko and H. Wang},
     title = {Antisymmetric paramodular forms of weight~3},
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V. A. Gritsenko; H. Wang. Antisymmetric paramodular forms of weight~3. Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1702-1723. http://geodesic.mathdoc.fr/item/SM_2019_210_12_a2/